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Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
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Tags: math, number theory Correct Solution: ``` # ---------------------------iye ha aam zindegi--------------------------------------------- import math import heapq, bisect import sys from collections import deque, defaultdict from fractions import Fraction mod = 10 ** 9 + 7 mod1 = 998244353 # ------------------------------warmup---------------------------- import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # -------------------game starts now----------------------------------------------------import math class TreeNode: def __init__(self, k, v): self.key = k self.value = v self.left = None self.right = None self.parent = None self.height = 1 self.num_left = 1 self.num_total = 1 class AvlTree: def __init__(self): self._tree = None def add(self, k, v): if not self._tree: self._tree = TreeNode(k, v) return node = self._add(k, v) if node: self._rebalance(node) def _add(self, k, v): node = self._tree while node: if k < node.key: if node.left: node = node.left else: node.left = TreeNode(k, v) node.left.parent = node return node.left elif node.key < k: if node.right: node = node.right else: node.right = TreeNode(k, v) node.right.parent = node return node.right else: node.value = v return @staticmethod def get_height(x): return x.height if x else 0 @staticmethod def get_num_total(x): return x.num_total if x else 0 def _rebalance(self, node): n = node while n: lh = self.get_height(n.left) rh = self.get_height(n.right) n.height = max(lh, rh) + 1 balance_factor = lh - rh n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right) n.num_left = 1 + self.get_num_total(n.left) if balance_factor > 1: if self.get_height(n.left.left) < self.get_height(n.left.right): self._rotate_left(n.left) self._rotate_right(n) elif balance_factor < -1: if self.get_height(n.right.right) < self.get_height(n.right.left): self._rotate_right(n.right) self._rotate_left(n) else: n = n.parent def _remove_one(self, node): """ Side effect!!! Changes node. Node should have exactly one child """ replacement = node.left or node.right if node.parent: if AvlTree._is_left(node): node.parent.left = replacement else: node.parent.right = replacement replacement.parent = node.parent node.parent = None else: self._tree = replacement replacement.parent = None node.left = None node.right = None node.parent = None self._rebalance(replacement) def _remove_leaf(self, node): if node.parent: if AvlTree._is_left(node): node.parent.left = None else: node.parent.right = None self._rebalance(node.parent) else: self._tree = None node.parent = None node.left = None node.right = None def remove(self, k): node = self._get_node(k) if not node: return if AvlTree._is_leaf(node): self._remove_leaf(node) return if node.left and node.right: nxt = AvlTree._get_next(node) node.key = nxt.key node.value = nxt.value if self._is_leaf(nxt): self._remove_leaf(nxt) else: self._remove_one(nxt) self._rebalance(node) else: self._remove_one(node) def get(self, k): node = self._get_node(k) return node.value if node else -1 def _get_node(self, k): if not self._tree: return None node = self._tree while node: if k < node.key: node = node.left elif node.key < k: node = node.right else: return node return None def get_at(self, pos): x = pos + 1 node = self._tree while node: if x < node.num_left: node = node.left elif node.num_left < x: x -= node.num_left node = node.right else: return (node.key, node.value) raise IndexError("Out of ranges") @staticmethod def _is_left(node): return node.parent.left and node.parent.left == node @staticmethod def _is_leaf(node): return node.left is None and node.right is None def _rotate_right(self, node): if not node.parent: self._tree = node.left node.left.parent = None elif AvlTree._is_left(node): node.parent.left = node.left node.left.parent = node.parent else: node.parent.right = node.left node.left.parent = node.parent bk = node.left.right node.left.right = node node.parent = node.left node.left = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) def _rotate_left(self, node): if not node.parent: self._tree = node.right node.right.parent = None elif AvlTree._is_left(node): node.parent.left = node.right node.right.parent = node.parent else: node.parent.right = node.right node.right.parent = node.parent bk = node.right.left node.right.left = node node.parent = node.right node.right = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) @staticmethod def _get_next(node): if not node.right: return node.parent n = node.right while n.left: n = n.left return n avl=AvlTree() #-----------------------------------------------binary seacrh tree--------------------------------------- class SegmentTree1: def __init__(self, data, default='z', func=lambda a, b: min(a ,b)): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------game starts now----------------------------------------------------import math class SegmentTree: def __init__(self, data, default=0, func=lambda a, b: a + b): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------------------iye ha chutiya zindegi------------------------------------- class Factorial: def __init__(self, MOD): self.MOD = MOD self.factorials = [1, 1] self.invModulos = [0, 1] self.invFactorial_ = [1, 1] def calc(self, n): if n <= -1: print("Invalid argument to calculate n!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.factorials): return self.factorials[n] nextArr = [0] * (n + 1 - len(self.factorials)) initialI = len(self.factorials) prev = self.factorials[-1] m = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = prev * i % m self.factorials += nextArr return self.factorials[n] def inv(self, n): if n <= -1: print("Invalid argument to calculate n^(-1)") print("n must be non-negative value. But the argument was " + str(n)) exit() p = self.MOD pi = n % p if pi < len(self.invModulos): return self.invModulos[pi] nextArr = [0] * (n + 1 - len(self.invModulos)) initialI = len(self.invModulos) for i in range(initialI, min(p, n + 1)): next = -self.invModulos[p % i] * (p // i) % p self.invModulos.append(next) return self.invModulos[pi] def invFactorial(self, n): if n <= -1: print("Invalid argument to calculate (n^(-1))!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.invFactorial_): return self.invFactorial_[n] self.inv(n) # To make sure already calculated n^-1 nextArr = [0] * (n + 1 - len(self.invFactorial_)) initialI = len(self.invFactorial_) prev = self.invFactorial_[-1] p = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p self.invFactorial_ += nextArr return self.invFactorial_[n] class Combination: def __init__(self, MOD): self.MOD = MOD self.factorial = Factorial(MOD) def ncr(self, n, k): if k < 0 or n < k: return 0 k = min(k, n - k) f = self.factorial return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD # --------------------------------------iye ha combinations ka zindegi--------------------------------- def powm(a, n, m): if a == 1 or n == 0: return 1 if n % 2 == 0: s = powm(a, n // 2, m) return s * s % m else: return a * powm(a, n - 1, m) % m # --------------------------------------iye ha power ka zindegi--------------------------------- def sort_list(list1, list2): zipped_pairs = zip(list2, list1) z = [x for _, x in sorted(zipped_pairs)] return z # --------------------------------------------------product---------------------------------------- def product(l): por = 1 for i in range(len(l)): por *= l[i] return por # --------------------------------------------------binary---------------------------------------- def binarySearchCount(arr, n, key): left = 0 right = n - 1 count = 0 while (left <= right): mid = int((right + left)/ 2) # Check if middle element is # less than or equal to key if (arr[mid]<=key): count = mid+1 left = mid + 1 # If key is smaller, ignore right half else: right = mid - 1 return count # --------------------------------------------------binary---------------------------------------- def countdig(n): c = 0 while (n > 0): n //= 10 c += 1 return c def countGreater( arr,n, k): l = 0 r = n - 1 # Stores the index of the left most element # from the array which is greater than k leftGreater = n # Finds number of elements greater than k while (l <= r): m = int(l + (r - l) / 2) if (arr[m] >= k): leftGreater = m r = m - 1 # If mid element is less than # or equal to k update l else: l = m + 1 # Return the count of elements # greater than k return (n - leftGreater) # --------------------------------------------------binary------------------------------------ for i in range(int(input())): a,b=map(int,input().split()) #c=a*b l=int((a*b)**(1/3)+0.5) if l**3==a*b and a%l==0 and b%l==0: print("YES") else: print("NO") ```
output
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Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
instruction
0
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19
14,422
Tags: math, number theory Correct Solution: ``` import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------------------ def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0 def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0 def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) mod = 998244353 INF = float('inf') from math import factorial from collections import Counter, defaultdict, deque from heapq import heapify, heappop, heappush from math import pow # ------------------------------ def main(): for _ in range(N()): a, b = RL() mt = a*b res = round(pow(mt, 1/3)) if res**3==mt and a%res==0 and b%res==0: print('Yes') else: print('No') if __name__ == "__main__": main() ```
output
1
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Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
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Tags: math, number theory Correct Solution: ``` # ---------------------------iye ha aam zindegi--------------------------------------------- import math import heapq, bisect import sys from collections import deque, defaultdict from fractions import Fraction mod = 10 ** 9 + 7 mod1 = 998244353 # ------------------------------warmup---------------------------- import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # -------------------game starts now----------------------------------------------------import math class TreeNode: def __init__(self, k, v): self.key = k self.value = v self.left = None self.right = None self.parent = None self.height = 1 self.num_left = 1 self.num_total = 1 class AvlTree: def __init__(self): self._tree = None def add(self, k, v): if not self._tree: self._tree = TreeNode(k, v) return node = self._add(k, v) if node: self._rebalance(node) def _add(self, k, v): node = self._tree while node: if k < node.key: if node.left: node = node.left else: node.left = TreeNode(k, v) node.left.parent = node return node.left elif node.key < k: if node.right: node = node.right else: node.right = TreeNode(k, v) node.right.parent = node return node.right else: node.value = v return @staticmethod def get_height(x): return x.height if x else 0 @staticmethod def get_num_total(x): return x.num_total if x else 0 def _rebalance(self, node): n = node while n: lh = self.get_height(n.left) rh = self.get_height(n.right) n.height = max(lh, rh) + 1 balance_factor = lh - rh n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right) n.num_left = 1 + self.get_num_total(n.left) if balance_factor > 1: if self.get_height(n.left.left) < self.get_height(n.left.right): self._rotate_left(n.left) self._rotate_right(n) elif balance_factor < -1: if self.get_height(n.right.right) < self.get_height(n.right.left): self._rotate_right(n.right) self._rotate_left(n) else: n = n.parent def _remove_one(self, node): """ Side effect!!! Changes node. Node should have exactly one child """ replacement = node.left or node.right if node.parent: if AvlTree._is_left(node): node.parent.left = replacement else: node.parent.right = replacement replacement.parent = node.parent node.parent = None else: self._tree = replacement replacement.parent = None node.left = None node.right = None node.parent = None self._rebalance(replacement) def _remove_leaf(self, node): if node.parent: if AvlTree._is_left(node): node.parent.left = None else: node.parent.right = None self._rebalance(node.parent) else: self._tree = None node.parent = None node.left = None node.right = None def remove(self, k): node = self._get_node(k) if not node: return if AvlTree._is_leaf(node): self._remove_leaf(node) return if node.left and node.right: nxt = AvlTree._get_next(node) node.key = nxt.key node.value = nxt.value if self._is_leaf(nxt): self._remove_leaf(nxt) else: self._remove_one(nxt) self._rebalance(node) else: self._remove_one(node) def get(self, k): node = self._get_node(k) return node.value if node else -1 def _get_node(self, k): if not self._tree: return None node = self._tree while node: if k < node.key: node = node.left elif node.key < k: node = node.right else: return node return None def get_at(self, pos): x = pos + 1 node = self._tree while node: if x < node.num_left: node = node.left elif node.num_left < x: x -= node.num_left node = node.right else: return (node.key, node.value) raise IndexError("Out of ranges") @staticmethod def _is_left(node): return node.parent.left and node.parent.left == node @staticmethod def _is_leaf(node): return node.left is None and node.right is None def _rotate_right(self, node): if not node.parent: self._tree = node.left node.left.parent = None elif AvlTree._is_left(node): node.parent.left = node.left node.left.parent = node.parent else: node.parent.right = node.left node.left.parent = node.parent bk = node.left.right node.left.right = node node.parent = node.left node.left = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) def _rotate_left(self, node): if not node.parent: self._tree = node.right node.right.parent = None elif AvlTree._is_left(node): node.parent.left = node.right node.right.parent = node.parent else: node.parent.right = node.right node.right.parent = node.parent bk = node.right.left node.right.left = node node.parent = node.right node.right = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) @staticmethod def _get_next(node): if not node.right: return node.parent n = node.right while n.left: n = n.left return n avl=AvlTree() #-----------------------------------------------binary seacrh tree--------------------------------------- class SegmentTree1: def __init__(self, data, default='z', func=lambda a, b: min(a ,b)): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------game starts now----------------------------------------------------import math class SegmentTree: def __init__(self, data, default=0, func=lambda a, b: a + b): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------------------iye ha chutiya zindegi------------------------------------- class Factorial: def __init__(self, MOD): self.MOD = MOD self.factorials = [1, 1] self.invModulos = [0, 1] self.invFactorial_ = [1, 1] def calc(self, n): if n <= -1: print("Invalid argument to calculate n!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.factorials): return self.factorials[n] nextArr = [0] * (n + 1 - len(self.factorials)) initialI = len(self.factorials) prev = self.factorials[-1] m = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = prev * i % m self.factorials += nextArr return self.factorials[n] def inv(self, n): if n <= -1: print("Invalid argument to calculate n^(-1)") print("n must be non-negative value. But the argument was " + str(n)) exit() p = self.MOD pi = n % p if pi < len(self.invModulos): return self.invModulos[pi] nextArr = [0] * (n + 1 - len(self.invModulos)) initialI = len(self.invModulos) for i in range(initialI, min(p, n + 1)): next = -self.invModulos[p % i] * (p // i) % p self.invModulos.append(next) return self.invModulos[pi] def invFactorial(self, n): if n <= -1: print("Invalid argument to calculate (n^(-1))!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.invFactorial_): return self.invFactorial_[n] self.inv(n) # To make sure already calculated n^-1 nextArr = [0] * (n + 1 - len(self.invFactorial_)) initialI = len(self.invFactorial_) prev = self.invFactorial_[-1] p = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p self.invFactorial_ += nextArr return self.invFactorial_[n] class Combination: def __init__(self, MOD): self.MOD = MOD self.factorial = Factorial(MOD) def ncr(self, n, k): if k < 0 or n < k: return 0 k = min(k, n - k) f = self.factorial return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD # --------------------------------------iye ha combinations ka zindegi--------------------------------- def powm(a, n, m): if a == 1 or n == 0: return 1 if n % 2 == 0: s = powm(a, n // 2, m) return s * s % m else: return a * powm(a, n - 1, m) % m # --------------------------------------iye ha power ka zindegi--------------------------------- def sort_list(list1, list2): zipped_pairs = zip(list2, list1) z = [x for _, x in sorted(zipped_pairs)] return z # --------------------------------------------------product---------------------------------------- def product(l): por = 1 for i in range(len(l)): por *= l[i] return por # --------------------------------------------------binary---------------------------------------- def binarySearchCount(arr, n, key): left = 0 right = n - 1 count = 0 while (left <= right): mid = int((right + left)/ 2) # Check if middle element is # less than or equal to key if (arr[mid]<=key): count = mid+1 left = mid + 1 # If key is smaller, ignore right half else: right = mid - 1 return count # --------------------------------------------------binary---------------------------------------- def countdig(n): c = 0 while (n > 0): n //= 10 c += 1 return c def countGreater( arr,n, k): l = 0 r = n - 1 # Stores the index of the left most element # from the array which is greater than k leftGreater = n # Finds number of elements greater than k while (l <= r): m = int(l + (r - l) / 2) if (arr[m] >= k): leftGreater = m r = m - 1 # If mid element is less than # or equal to k update l else: l = m + 1 # Return the count of elements # greater than k return (n - leftGreater) # --------------------------------------------------binary------------------------------------ for i in range(int(input())): a,b=map(int,input().split()) c=a*b l=int(c**(1/3)+0.5) if l**3==a*b and a%l==0 and b%l==0: print("YES") else: print("NO") ```
output
1
7,212
19
14,425
Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
instruction
0
7,213
19
14,426
Tags: math, number theory Correct Solution: ``` import os, sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") for _ in range(int(input())): a, b = map(int, input().split()) q = a * b t = round(q ** (1 / 3)) if t * t * t == q and a % t == b % t == 0: print('YES') else: print('NO') ```
output
1
7,213
19
14,427
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. Submitted Solution: ``` import sys input = sys.stdin.buffer.readline def gcd(a, b): if a > b: a, b = b, a if b % a==0: return a return gcd(b % a, a) def process(a, b): g = gcd(a, b) r = a//g s = b//g if g % r != 0: return 'No' g = g//r if g % s != 0: return 'No' G3 = g//s G = round(G3**(1/3)) cube = False for i in range(10): if (G-i)**3==G3 or (G+i)**3==G3: cube = True break if not cube: return 'No' return 'Yes' n = int(input()) for i in range(n): a, b = [int(x) for x in input().split()] sys.stdout.write(process(a, b)+'\n') ```
instruction
0
7,214
19
14,428
Yes
output
1
7,214
19
14,429
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. Submitted Solution: ``` import io import os input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline t = int(input()) for tc in range(t): a, b = map(int, input().split()) cbrt = round(pow(a*b, 1/3)) if pow(cbrt, 3) == a*b: if a % cbrt == b % cbrt == 0: print("Yes") continue print("No") ```
instruction
0
7,215
19
14,430
Yes
output
1
7,215
19
14,431
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. Submitted Solution: ``` # ---------------------------iye ha aam zindegi--------------------------------------------- import math import heapq, bisect import sys from collections import deque, defaultdict from fractions import Fraction mod = 10 ** 9 + 7 mod1 = 998244353 # ------------------------------warmup---------------------------- import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # -------------------game starts now----------------------------------------------------import math class TreeNode: def __init__(self, k, v): self.key = k self.value = v self.left = None self.right = None self.parent = None self.height = 1 self.num_left = 1 self.num_total = 1 class AvlTree: def __init__(self): self._tree = None def add(self, k, v): if not self._tree: self._tree = TreeNode(k, v) return node = self._add(k, v) if node: self._rebalance(node) def _add(self, k, v): node = self._tree while node: if k < node.key: if node.left: node = node.left else: node.left = TreeNode(k, v) node.left.parent = node return node.left elif node.key < k: if node.right: node = node.right else: node.right = TreeNode(k, v) node.right.parent = node return node.right else: node.value = v return @staticmethod def get_height(x): return x.height if x else 0 @staticmethod def get_num_total(x): return x.num_total if x else 0 def _rebalance(self, node): n = node while n: lh = self.get_height(n.left) rh = self.get_height(n.right) n.height = max(lh, rh) + 1 balance_factor = lh - rh n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right) n.num_left = 1 + self.get_num_total(n.left) if balance_factor > 1: if self.get_height(n.left.left) < self.get_height(n.left.right): self._rotate_left(n.left) self._rotate_right(n) elif balance_factor < -1: if self.get_height(n.right.right) < self.get_height(n.right.left): self._rotate_right(n.right) self._rotate_left(n) else: n = n.parent def _remove_one(self, node): """ Side effect!!! Changes node. Node should have exactly one child """ replacement = node.left or node.right if node.parent: if AvlTree._is_left(node): node.parent.left = replacement else: node.parent.right = replacement replacement.parent = node.parent node.parent = None else: self._tree = replacement replacement.parent = None node.left = None node.right = None node.parent = None self._rebalance(replacement) def _remove_leaf(self, node): if node.parent: if AvlTree._is_left(node): node.parent.left = None else: node.parent.right = None self._rebalance(node.parent) else: self._tree = None node.parent = None node.left = None node.right = None def remove(self, k): node = self._get_node(k) if not node: return if AvlTree._is_leaf(node): self._remove_leaf(node) return if node.left and node.right: nxt = AvlTree._get_next(node) node.key = nxt.key node.value = nxt.value if self._is_leaf(nxt): self._remove_leaf(nxt) else: self._remove_one(nxt) self._rebalance(node) else: self._remove_one(node) def get(self, k): node = self._get_node(k) return node.value if node else -1 def _get_node(self, k): if not self._tree: return None node = self._tree while node: if k < node.key: node = node.left elif node.key < k: node = node.right else: return node return None def get_at(self, pos): x = pos + 1 node = self._tree while node: if x < node.num_left: node = node.left elif node.num_left < x: x -= node.num_left node = node.right else: return (node.key, node.value) raise IndexError("Out of ranges") @staticmethod def _is_left(node): return node.parent.left and node.parent.left == node @staticmethod def _is_leaf(node): return node.left is None and node.right is None def _rotate_right(self, node): if not node.parent: self._tree = node.left node.left.parent = None elif AvlTree._is_left(node): node.parent.left = node.left node.left.parent = node.parent else: node.parent.right = node.left node.left.parent = node.parent bk = node.left.right node.left.right = node node.parent = node.left node.left = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) def _rotate_left(self, node): if not node.parent: self._tree = node.right node.right.parent = None elif AvlTree._is_left(node): node.parent.left = node.right node.right.parent = node.parent else: node.parent.right = node.right node.right.parent = node.parent bk = node.right.left node.right.left = node node.parent = node.right node.right = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) @staticmethod def _get_next(node): if not node.right: return node.parent n = node.right while n.left: n = n.left return n avl=AvlTree() #-----------------------------------------------binary seacrh tree--------------------------------------- class SegmentTree1: def __init__(self, data, default='z', func=lambda a, b: min(a ,b)): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------game starts now----------------------------------------------------import math class SegmentTree: def __init__(self, data, default=0, func=lambda a, b: a + b): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------------------iye ha chutiya zindegi------------------------------------- class Factorial: def __init__(self, MOD): self.MOD = MOD self.factorials = [1, 1] self.invModulos = [0, 1] self.invFactorial_ = [1, 1] def calc(self, n): if n <= -1: print("Invalid argument to calculate n!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.factorials): return self.factorials[n] nextArr = [0] * (n + 1 - len(self.factorials)) initialI = len(self.factorials) prev = self.factorials[-1] m = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = prev * i % m self.factorials += nextArr return self.factorials[n] def inv(self, n): if n <= -1: print("Invalid argument to calculate n^(-1)") print("n must be non-negative value. But the argument was " + str(n)) exit() p = self.MOD pi = n % p if pi < len(self.invModulos): return self.invModulos[pi] nextArr = [0] * (n + 1 - len(self.invModulos)) initialI = len(self.invModulos) for i in range(initialI, min(p, n + 1)): next = -self.invModulos[p % i] * (p // i) % p self.invModulos.append(next) return self.invModulos[pi] def invFactorial(self, n): if n <= -1: print("Invalid argument to calculate (n^(-1))!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.invFactorial_): return self.invFactorial_[n] self.inv(n) # To make sure already calculated n^-1 nextArr = [0] * (n + 1 - len(self.invFactorial_)) initialI = len(self.invFactorial_) prev = self.invFactorial_[-1] p = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p self.invFactorial_ += nextArr return self.invFactorial_[n] class Combination: def __init__(self, MOD): self.MOD = MOD self.factorial = Factorial(MOD) def ncr(self, n, k): if k < 0 or n < k: return 0 k = min(k, n - k) f = self.factorial return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD # --------------------------------------iye ha combinations ka zindegi--------------------------------- def powm(a, n, m): if a == 1 or n == 0: return 1 if n % 2 == 0: s = powm(a, n // 2, m) return s * s % m else: return a * powm(a, n - 1, m) % m # --------------------------------------iye ha power ka zindegi--------------------------------- def sort_list(list1, list2): zipped_pairs = zip(list2, list1) z = [x for _, x in sorted(zipped_pairs)] return z # --------------------------------------------------product---------------------------------------- def product(l): por = 1 for i in range(len(l)): por *= l[i] return por # --------------------------------------------------binary---------------------------------------- def binarySearchCount(arr, n, key): left = 0 right = n - 1 count = 0 while (left <= right): mid = int((right + left)/ 2) # Check if middle element is # less than or equal to key if (arr[mid]<=key): count = mid+1 left = mid + 1 # If key is smaller, ignore right half else: right = mid - 1 return count # --------------------------------------------------binary---------------------------------------- def countdig(n): c = 0 while (n > 0): n //= 10 c += 1 return c def countGreater( arr,n, k): l = 0 r = n - 1 # Stores the index of the left most element # from the array which is greater than k leftGreater = n # Finds number of elements greater than k while (l <= r): m = int(l + (r - l) / 2) if (arr[m] >= k): leftGreater = m r = m - 1 # If mid element is less than # or equal to k update l else: l = m + 1 # Return the count of elements # greater than k return (n - leftGreater) # --------------------------------------------------binary------------------------------------ for i in range(int(input())): a,b=map(int,input().split()) l=(a*b)**(Fraction(1,3))+0.5 if int(l)**3==a*b and a%l==0 and b%l==0: print("YES") else: print("NO") ```
instruction
0
7,216
19
14,432
No
output
1
7,216
19
14,433
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. Submitted Solution: ``` primes = [] M = 10**9 for p in range(2, M): if p*p > M: break is_prime = True for p2 in primes: if p2*p2 > p: break if p % p2==0: is_prime = False break if is_prime: primes.append(p) def factor(n): d = {} for p in primes: if p*p > n: break if n % p==0: c = 0 while n % p==0: c+=1 n = n//p d[p] = c if n > 1: d[n] = 1 return d def process(a, b): d1 = factor(a) d2 = factor(b) L = [] for p in d1: L.append(p) for p in d2: if p not in d1: L.append(p) for p in L: x = d1.get(p, 0) y = d2.get(p, 0) if (x+y) % 3 != 0: return 'No' if x < 2*y or y < 2*x: return 'No' return 'Yes' n = int(input()) for i in range(n): a, b = [int(x) for x in input().split()] print(process(a, b)) ```
instruction
0
7,217
19
14,434
No
output
1
7,217
19
14,435
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. Submitted Solution: ``` n = int(input()) for _ in range (n): a, b = map(int, input().split()) p = a * b c = int(round(p ** .333)) if c ** 3 == p and a % c == 0 and b % c == 0: print("Yes") else: print("No") ```
instruction
0
7,218
19
14,436
No
output
1
7,218
19
14,437
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≀ n ≀ 350000) is given. Each game is represented by a pair of scores a, b (1 ≀ a, b ≀ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. Submitted Solution: ``` import math t = int(input()) for tc in range(t): a, b = map(int, input().split()) if not round(pow(a*b, 1/3), 2) ** 3 != a*b: if a % round(pow(a*b, 1/3), 2) == b % round(pow(a*b, 1/3), 2) == 0: print("Yes") continue print("No") ```
instruction
0
7,219
19
14,438
No
output
1
7,219
19
14,439
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
0
7,266
19
14,532
Tags: dp Correct Solution: ``` from __future__ import print_function from queue import Queue import sys import math import os.path # CONFIG sys.setrecursionlimit(10**9) # LOG def log(*args, **kwargs): print(*args, file=sys.stderr, **kwargs) # INPUT def ni(): return map(int, input().split()) def nio(offset): return map(lambda x: int(x) + offset, input().split()) def nia(): return list(map(int, input().split())) # CONVERT def toString(aList, sep=" "): return sep.join(str(x) for x in aList) def mapInvertIndex(aList): return {k: v for v, k in enumerate(aList)} def countMap(arr): m = {} for x in arr: m[x] = m.get(x,0) + 1 return m def sortId(arr): return sorted(range(arr), key=lambda k: arr[k]) # MAIN n, k = ni() c = nia() f = nia() h = [0] + (nia()) cc = countMap(c) cf = countMap(f) n1 = n+1 k1 = k+1 nk1 = n*k+1 dp = [[0]*nk1 for _ in range(n1)] for ni in range(1,n1): for ki in range(1,nk1): mficount = min(k,ki) + 1 for kii in range(mficount): # log(ni,ki, kii, dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) dp[ni][ki] = max(dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) # log(dp[ni]) # log(n,k) # log("c", cc) # log("f", cf) # log("h", h) # log(dp) res = 0 for fk,fv in cf.items(): # log(fk, fv, cc.get(fk,0)) res += dp[fv][cc.get(fk,0)] print(res) ```
output
1
7,266
19
14,533
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
0
7,267
19
14,534
Tags: dp Correct Solution: ``` def solve(): n, k = map(int, input().split()) c = list(map(int, input().split())) f = list(map(int, input().split())) h = list(map(int, input().split())) cnt = {} for i in c: cnt[i] = cnt.get(i, 0) + 1 likecolor = {} for i in range(n): likecolor.setdefault(f[i], []).append(i) cnt[f[i]] = cnt.get(f[i], 0) ans = 0 for key, v in likecolor.items(): n1 = len(v) if cnt[key] >= n1 * k: ans += n1 * h[k - 1] continue dp = [[-float("INF")] * (cnt[key]+1) for _ in range(n1 + 1)] dp[0][0] = 0 for i in range(n1): j = i + 1 for e in range(cnt[key] + 1): dp[j][e] = max(dp[j][e], dp[i][e]) for w in range(e + 1, min(cnt[key] + 1, e + k + 1)): dp[j][w] = max(dp[i][e] + h[w - e - 1], dp[j][w]) ans += dp[n1][cnt[key]] print(ans) solve() ```
output
1
7,267
19
14,535
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
0
7,268
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Tags: dp Correct Solution: ``` from __future__ import print_function from queue import Queue import sys import math import os.path sys.setrecursionlimit(10**9) def log(*args, **kwargs): print(*args, file=sys.stderr, **kwargs) def ni(): return map(int, input().split()) def nio(offset): return map(lambda x: int(x) + offset, input().split()) def nia(): return list(map(int, input().split())) def toString(aList, sep=" "): return sep.join(str(x) for x in aList) def mapInvertIndex(aList): return {k: v for v, k in enumerate(aList)} def countMap(arr): m = {} for x in arr: m[x] = m.get(x,0) + 1 return m def sortId(arr): return sorted(range(arr), key=lambda k: arr[k]) # MAIN n, k = ni() c = nia() f = nia() h = nia() h.insert(0,0) cc = countMap(c) cf = countMap(f) n1 = n+1 k1 = k+1 nk1 = n*k+1 dp = [[0]*nk1 for _ in range(n1)] for ni in range(1,n1): for ki in range(1,nk1): mficount = min(k,ki) + 1 for kii in range(mficount): dp[ni][ki] = max(dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) res = 0 for fk,fv in cf.items(): res += dp[fv][cc.get(fk,0)] print(res) ```
output
1
7,268
19
14,537
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
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Tags: dp Correct Solution: ``` n,k= map(int,input().split(' ')) l= list(map(int,input().split(' '))) f =list(map(int,input().split(' '))) h=list(map(int,input().split(' '))) d1=dict({(a,0) for a in f}) d2=dict({(a,0) for a in f}) for a in l: if(a in d1):d1[a]+=1 for a in f: d2[a]+=1 #print(d1,d2) dp = [[0 for i in range(520*12)] for j in range(520)] #print(len(dp), len(dp[0])) for x in range(n+1): for y in range(n*k+1): for i in range(k+1): dp[x+1][y+i] = max(dp[x+1][y+i],+dp[x][y]+(0 if i==0 else h[i-1]) ) ss=0 for i in d1: #print(dp[d1[i]][d2[i]]) ss+=dp[d2[i]][d1[i]] print(ss) ```
output
1
7,269
19
14,539
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
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Tags: dp Correct Solution: ``` import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------------------ def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0 def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0 def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) mod = 998244353 INF = float('inf') from math import factorial from collections import Counter, defaultdict, deque from heapq import heapify, heappop, heappush # ------------------------------ # f = open('./input.txt') # sys.stdin = f def main(): n, k = RL() cds = RLL() fn = RLL() sc = [0]+RLL() rec = set(fn) uses = 0 dic = defaultdict(int) for i in cds: if i in rec: dic[i]+=1 uses+=1 dp = [[0]*(n*k+1) for _ in range(n+1)] for i in range(1, n+1): for j in range(1, n*k+1): for l in range(k+1): if l>j: break val = sc[l] dp[i][j] = max(dp[i][j], dp[i-1][j-l]+val) res = 0 for i, v in Counter(fn).items(): res+=dp[v][dic[i]] # for i in dp: print(i) print(res) if __name__ == "__main__": main() ```
output
1
7,270
19
14,541
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
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Tags: dp Correct Solution: ``` # by the authority of GOD author: manhar singh sachdev # import os,sys from io import BytesIO,IOBase def main(): n,k = map(int,input().split()) card = list(map(int,input().split())) fav = list(map(int,input().split())) joy = [0]+list(map(int,input().split())) dp = [[0]*(n*k+1) for _ in range(n+1)] for i in range(len(joy)): dp[1][i] = joy[i] for i in range(len(joy),n*k+1): dp[1][i] = joy[-1] for i in range(2,n+1): for j in range(1,n*k+1): for kk in range(min(k+1,j+1)): dp[i][j] = max(dp[i][j],dp[i-1][j-kk]+dp[1][kk]) tot = [0]*(10**5+1) for i in card: tot[i] += 1 tot1 = [0]*(10**5+1) for i in fav: tot1[i] += 1 ans = 0 for i in range(10**5+1): ans += dp[tot1[i]][tot[i]] print(ans) #Fast IO Region BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") if __name__ == '__main__': main() ```
output
1
7,271
19
14,543
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
0
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Tags: dp Correct Solution: ``` import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------------------ def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0 def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0 def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) mod = 998244353 INF = float('inf') from math import factorial from collections import Counter, defaultdict, deque from heapq import heapify, heappop, heappush # ------------------------------ # f = open('./input.txt') # sys.stdin = f def main(): n, k = RL() cds = RLL() fn = RLL() sc = [0]+RLL() rec = set(fn) uses = 0 dic = defaultdict(int) for i in cds: if i in rec: dic[i]+=1 uses+=1 dp = [[0]*(uses+1) for _ in range(n+1)] for i in range(1, n+1): for j in range(1, uses+1): for l in range(k+1): if l>j: break val = sc[l] dp[i][j] = max(dp[i][j], dp[i-1][j-l]+val) res = 0 for i, v in Counter(fn).items(): res+=dp[v][dic[i]] # for i in dp: print(i) print(res) if __name__ == "__main__": main() ```
output
1
7,272
19
14,545
Provide tags and a correct Python 3 solution for this coding contest problem. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
instruction
0
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Tags: dp Correct Solution: ``` from __future__ import print_function from queue import Queue import sys import math import os.path # CONFIG sys.setrecursionlimit(10**9) # LOG def log(*args, **kwargs): print(*args, file=sys.stderr, **kwargs) # INPUT def ni(): return map(int, input().split()) def nio(offset): return map(lambda x: int(x) + offset, input().split()) def nia(): return list(map(int, input().split())) # CONVERT def toString(aList, sep=" "): return sep.join(str(x) for x in aList) def mapInvertIndex(aList): return {k: v for v, k in enumerate(aList)} def countMap(arr): m = {} for x in arr: m[x] = m.get(x,0) + 1 return m def sortId(arr): return sorted(range(arr), key=lambda k: arr[k]) # MAIN n, k = ni() c = nia() f = nia() h = [0] h.extend(nia()) cc = countMap(c) cf = countMap(f) n1 = n+1 k1 = k+1 nk1 = n*k+1 dp = [[0]*nk1 for _ in range(n1)] for ni in range(1,n1): for ki in range(1,nk1): mficount = min(k,ki) + 1 for kii in range(mficount): # log(ni,ki, kii, dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) dp[ni][ki] = max(dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) # log(dp[ni]) # log(n,k) # log("c", cc) # log("f", cf) # log("h", h) # log(dp) res = 0 for fk,fv in cf.items(): # log(fk, fv, cc.get(fk,0)) res += dp[fv][cc.get(fk,0)] print(res) ```
output
1
7,273
19
14,547
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` from __future__ import print_function from collections import Counter from queue import Queue import sys import math import os.path # CONFIG sys.setrecursionlimit(10**9) # LOG def log(*args, **kwargs): print(*args, file=sys.stderr, **kwargs) # INPUT def ni(): return map(int, input().split()) def nio(offset): return map(lambda x: int(x) + offset, input().split()) def nia(): return list(map(int, input().split())) # CONVERT def toString(aList, sep=" "): return sep.join(str(x) for x in aList) def mapInvertIndex(aList): return {k: v for v, k in enumerate(aList)} def sortId(arr): return sorted(range(arr), key=lambda k: arr[k]) # MAIN n, k = ni() c = nia() f = nia() h = nia() h.insert(0,0) cc = Counter(c) cf = Counter(f) n1 = n+1 k1 = k+1 nk1 = n*k+1 dp = [[0]*nk1 for _ in range(n1)] for ni in range(1,n1): for ki in range(1,nk1): mficount = min(k,ki) + 1 for kii in range(mficount): # log(ni,ki, kii, dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) dp[ni][ki] = max(dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) # log(dp[ni]) # log(n,k) # log("c", cc) # log("f", cf) # log("h", h) # log(dp) res = 0 for fk,fv in cf.items(): # log(fk, fv, cc.get(fk,0)) res += dp[fv][cc.get(fk,0)] print(res) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` #Code by Sounak, IIESTS #------------------------------warmup---------------------------- import os import sys import math from io import BytesIO, IOBase import io from fractions import Fraction import collections from itertools import permutations from collections import defaultdict from collections import deque import threading #sys.setrecursionlimit(300000) #threading.stack_size(10**8) BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #------------------------------------------------------------------------- #mod = 9223372036854775807 class SegmentTree: def __init__(self, data, default=0, func=lambda a, b: a+b): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) class SegmentTree1: def __init__(self, data, default=10**6, func=lambda a, b: min(a,b)): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) MOD=10**9+7 class Factorial: def __init__(self, MOD): self.MOD = MOD self.factorials = [1, 1] self.invModulos = [0, 1] self.invFactorial_ = [1, 1] def calc(self, n): if n <= -1: print("Invalid argument to calculate n!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.factorials): return self.factorials[n] nextArr = [0] * (n + 1 - len(self.factorials)) initialI = len(self.factorials) prev = self.factorials[-1] m = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = prev * i % m self.factorials += nextArr return self.factorials[n] def inv(self, n): if n <= -1: print("Invalid argument to calculate n^(-1)") print("n must be non-negative value. But the argument was " + str(n)) exit() p = self.MOD pi = n % p if pi < len(self.invModulos): return self.invModulos[pi] nextArr = [0] * (n + 1 - len(self.invModulos)) initialI = len(self.invModulos) for i in range(initialI, min(p, n + 1)): next = -self.invModulos[p % i] * (p // i) % p self.invModulos.append(next) return self.invModulos[pi] def invFactorial(self, n): if n <= -1: print("Invalid argument to calculate (n^(-1))!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.invFactorial_): return self.invFactorial_[n] self.inv(n) # To make sure already calculated n^-1 nextArr = [0] * (n + 1 - len(self.invFactorial_)) initialI = len(self.invFactorial_) prev = self.invFactorial_[-1] p = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p self.invFactorial_ += nextArr return self.invFactorial_[n] class Combination: def __init__(self, MOD): self.MOD = MOD self.factorial = Factorial(MOD) def ncr(self, n, k): if k < 0 or n < k: return 0 k = min(k, n - k) f = self.factorial return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD mod=10**9+7 omod=998244353 #---------------------------------Lazy Segment Tree-------------------------------------- # https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp class LazySegTree: def __init__(self, _op, _e, _mapping, _composition, _id, v): def set(p, x): assert 0 <= p < _n p += _size for i in range(_log, 0, -1): _push(p >> i) _d[p] = x for i in range(1, _log + 1): _update(p >> i) def get(p): assert 0 <= p < _n p += _size for i in range(_log, 0, -1): _push(p >> i) return _d[p] def prod(l, r): assert 0 <= l <= r <= _n if l == r: return _e l += _size r += _size for i in range(_log, 0, -1): if ((l >> i) << i) != l: _push(l >> i) if ((r >> i) << i) != r: _push(r >> i) sml = _e smr = _e while l < r: if l & 1: sml = _op(sml, _d[l]) l += 1 if r & 1: r -= 1 smr = _op(_d[r], smr) l >>= 1 r >>= 1 return _op(sml, smr) def apply(l, r, f): assert 0 <= l <= r <= _n if l == r: return l += _size r += _size for i in range(_log, 0, -1): if ((l >> i) << i) != l: _push(l >> i) if ((r >> i) << i) != r: _push((r - 1) >> i) l2 = l r2 = r while l < r: if l & 1: _all_apply(l, f) l += 1 if r & 1: r -= 1 _all_apply(r, f) l >>= 1 r >>= 1 l = l2 r = r2 for i in range(1, _log + 1): if ((l >> i) << i) != l: _update(l >> i) if ((r >> i) << i) != r: _update((r - 1) >> i) def _update(k): _d[k] = _op(_d[2 * k], _d[2 * k + 1]) def _all_apply(k, f): _d[k] = _mapping(f, _d[k]) if k < _size: _lz[k] = _composition(f, _lz[k]) def _push(k): _all_apply(2 * k, _lz[k]) _all_apply(2 * k + 1, _lz[k]) _lz[k] = _id _n = len(v) _log = _n.bit_length() _size = 1 << _log _d = [_e] * (2 * _size) _lz = [_id] * _size for i in range(_n): _d[_size + i] = v[i] for i in range(_size - 1, 0, -1): _update(i) self.set = set self.get = get self.prod = prod self.apply = apply MIL = 1 << 20 def makeNode(total, count): # Pack a pair into a float return (total * MIL) + count def getTotal(node): return math.floor(node / MIL) def getCount(node): return node - getTotal(node) * MIL nodeIdentity = makeNode(0.0, 0.0) def nodeOp(node1, node2): return node1 + node2 # Equivalent to the following: return makeNode( getTotal(node1) + getTotal(node2), getCount(node1) + getCount(node2) ) identityMapping = -1 def mapping(tag, node): if tag == identityMapping: return node # If assigned, new total is the number assigned times count count = getCount(node) return makeNode(tag * count, count) def composition(mapping1, mapping2): # If assigned multiple times, take first non-identity assignment return mapping1 if mapping1 != identityMapping else mapping2 #------------------------------------------------------------------------- prime = [True for i in range(10)] pp=[0]*10 def SieveOfEratosthenes(n=10): p = 2 c=0 while (p * p <= n): if (prime[p] == True): c+=1 for i in range(p, n+1, p): pp[i]+=1 prime[i] = False p += 1 #---------------------------------Binary Search------------------------------------------ def binarySearch(arr, n, key): left = 0 right = n-1 mid = 0 res=arr[n-1] while (left <= right): mid = (right + left)//2 if (arr[mid] >= key): res=arr[mid] right = mid-1 else: left = mid + 1 return res def binarySearch1(arr, n, key): left = 0 right = n-1 mid = 0 res=arr[0] while (left <= right): mid = (right + left)//2 if (arr[mid] > key): right = mid-1 else: res=arr[mid] left = mid + 1 return res #---------------------------------running code------------------------------------------ n,k= map(int,input().split(' ')) l= list(map(int,input().split(' '))) f =list(map(int,input().split(' '))) h=list(map(int,input().split(' '))) d1=dict({(a,0) for a in f}) d2=dict({(a,0) for a in f}) for a in l: if(a in d1):d1[a]+=1 for a in f: d2[a]+=1 #print(d1,d2) dp = [[0 for i in range(520*12)] for j in range(520)] #print(len(dp), len(dp[0])) for x in range(n+1): for y in range(n*k+1): for i in range(k+1): dp[x+1][y+i] = max(dp[x+1][y+i],+dp[x][y]+(0 if i==0 else h[i-1]) ) ss=0 for i in d1: #print(dp[d1[i]][d2[i]]) ss+=dp[d2[i]][d1[i]] print(ss) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` import math from collections import defaultdict def main(): n, k = map(int, input().split()) cards = list(map(int, input().split())) fav = list(map(int, input().split())) h = [0] + list(map(int, input().split())) cards_cnt = defaultdict(int) for val in cards: cards_cnt[val] += 1 players_fav_cnt = defaultdict(int) for val in fav: players_fav_cnt[val] += 1 # dp[a][b] - a players, b favourite cards (in total) dp = [[0 for _ in range(k*n+k+1)] for _ in range(n+1)] for p in range(n): for c in range(k*n+1): for hand in range(k+1): dp[p+1][c+hand] = max(dp[p+1][c+hand], dp[p][c] + h[hand]) res = 0 for f in players_fav_cnt: res += dp[players_fav_cnt[f]][cards_cnt[f]] print(res) if __name__ == '__main__': main() ```
instruction
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Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` from __future__ import print_function from collections import Counter from queue import Queue import sys import math import os.path # CONFIG sys.setrecursionlimit(10**9) # LOG def log(*args, **kwargs): print(*args, file=sys.stderr, **kwargs) # INPUT def ni(): return map(int, input().split()) def nio(offset): return map(lambda x: int(x) + offset, input().split()) def nia(): return list(map(int, input().split())) # CONVERT def toString(aList, sep=" "): return sep.join(str(x) for x in aList) def mapInvertIndex(aList): return {k: v for v, k in enumerate(aList)} def sortId(arr): return sorted(range(arr), key=lambda k: arr[k]) # MAIN n, k = ni() c = nia() f = nia() h = nia() h.insert(0,0) cc = Counter(c) cf = Counter(f) n1 = n+1 k1 = k+1 nk1 = n*k+1 dp = [[0]*nk1 for _ in range(n1)] for ni in range(1,n1): for ki in range(1,nk1): mficount = min(k,ki) + 1 for kii in range(mficount): # log(ni,ki, kii, dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) dp[ni][ki] = max(dp[ni][ki], dp[ni-1][ki-kii] + h[kii]) # log(dp[ni]) # log(n,k) # log("c", cc) # log("f", cf) # log("h", h) # log(dp) res = 0 for fk,fv in cf.items(): # log(fk, fv, cc.get(fk,0)) res += dp[fv][cc[fk]] print(res) ```
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Yes
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19
14,555
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` DEBUG = False def dprint (*args, **kwargs): pass print (*args, **kwargs) if DEBUG: nk = "4 3" c = "1 3 2 8 5 5 8 2 2 8 5 2" f = "1 2 2 5" h = "2 6 7" else: nk = input() c = input() f = input() h = input() n, k = map(int, nk.split()) c = list(map(int, c.split())) f = list(map(int, f.split())) #n = len(f) #k = len(c) // n h = list(map(int, h.split())) znaki = set(c + f) # different card values in game # find supply and demand supply = {} demand = {} for z in znaki: supply[z] = c.count(z) demand[z] = f.count(z) dprint("supply:", supply) dprint("demand:", demand) # build H-matrix dm = max(demand.values()) sm = max(supply.values()) dprint (znaki, sm, dm) ''' if n == 4: print (21) elif n == 3: print (0) else: #map(int, c.split()) print (znaki, sm, dm) Π’Π²ΠΎΠ΄ 500 10 2 1 1 2 2 ... {1, 2} 2507 269 ΠžΡ‚Π²Π΅Ρ‚ 42588497 ''' def happy_1(num, pl): if num == 0: return 0 if pl == 0: return 0 if pl == 1: return h[min(num, k) - 1] if num == 1: return h[0] max_hap = 0 for i in range(1, min(num, k) + 1): hap = h[i - 1] + happy_1(num - i, pl - 1) if hap > max_hap: max_hap = hap return max_hap #dprint(happy_1(3, 1)) happy_matrix = [] for d in range(dm + 1): happy_row = [] for s in range(min (sm, dm*k) + 1): happy_row.append(happy_1(s, d)) # print(s, d, happy_1(s, d)) happy_matrix.append(happy_row) dprint("happy_matrix:", happy_matrix) # find H-functions deficit_sum = 0 for z in znaki: deficit = demand[z] * k - supply[z] deficit_sum += deficit dprint(z, deficit) #print("deficit_sum", deficit_sum) # reallocate cards # calculate result total_happy = 0 for z in znaki: total_happy += happy_matrix[demand[z]][min(supply[z], demand[z] * k)] print(total_happy) dprint("total_happy:", total_happy) ```
instruction
0
7,278
19
14,556
No
output
1
7,278
19
14,557
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` DEBUG = False def dprint(*args, **kwargs): if DEBUG: print("#>",*args, **kwargs) if DEBUG: nk = "4 3" c = "1 3 2 8 5 5 8 2 2 8 5 2" f = "1 2 2 5" h = "2 6 7" else: nk = input() c = input() f = input() h = input() n, k = map(int, nk.split()) c = list(map(int, c.split())) f = list(map(int, f.split())) # n = len(f) # k = len(c) // n h = list(map(int, h.split())) znaki_s = set(c) # different card values in supply znaki_d = set(f) # different card values in demand znaki = set(c + f) # different card values in game # find supply and demand supply = {} demand = {} for z in znaki_s: supply[z] = c.count(z) for z in znaki_d: demand[z] = f.count(z) dprint("supply:", supply) dprint("demand:", demand) # build H-matrix dm = max(demand.values()) sm = max(supply.values()) dprint(znaki, sm, dm) if n == 4: print (21) elif n == 3: print (0) else: print (n, k, znaki_s, f, h) ```
instruction
0
7,279
19
14,558
No
output
1
7,279
19
14,559
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------------------ def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0 def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0 def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) mod = 998244353 INF = float('inf') from math import factorial from collections import Counter, defaultdict, deque from heapq import heapify, heappop, heappush # ------------------------------ # f = open('./input.txt') # sys.stdin = f def main(): n, k = RL() cds = RLL() fn = RLL() sc = [0]+RLL() rec = set(fn) uses = 0 dic = defaultdict(int) for i in cds: if i in rec: dic[i]+=1 uses+=1 dp = [[0]*(uses+1) for _ in range(n+1)] for i in range(1, n+1): for j in range(1, uses+1): if j>i*k: break for l in range(k+1): if l>j: break val = sc[l] dp[i][j] = max(dp[i][j], dp[i-1][j-l]+val) res = 0 for i, v in Counter(fn).items(): res+=dp[v][dic[i]] print(res) if __name__ == "__main__": main() ```
instruction
0
7,280
19
14,560
No
output
1
7,280
19
14,561
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j. There are k β‹… n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below. The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0. Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players. Input The first line of input contains two integers n and k (1 ≀ n ≀ 500, 1 ≀ k ≀ 10) β€” the number of players and the number of cards each player will get. The second line contains k β‹… n integers c_1, c_2, ..., c_{k β‹… n} (1 ≀ c_i ≀ 10^5) β€” the numbers written on the cards. The third line contains n integers f_1, f_2, ..., f_n (1 ≀ f_j ≀ 10^5) β€” the favorite numbers of the players. The fourth line contains k integers h_1, h_2, ..., h_k (1 ≀ h_t ≀ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k]. Output Print one integer β€” the maximum possible total joy levels of the players among all possible card distributions. Examples Input 4 3 1 3 2 8 5 5 8 2 2 8 5 2 1 2 2 5 2 6 7 Output 21 Input 3 3 9 9 9 9 9 9 9 9 9 1 2 3 1 2 3 Output 0 Note In the first example, one possible optimal card distribution is the following: * Player 1 gets cards with numbers [1, 3, 8]; * Player 2 gets cards with numbers [2, 2, 8]; * Player 3 gets cards with numbers [2, 2, 8]; * Player 4 gets cards with numbers [5, 5, 5]. Thus, the answer is 2 + 6 + 6 + 7 = 21. In the second example, no player can get a card with his favorite number. Thus, the answer is 0. Submitted Solution: ``` DEBUG = False def dprint(*args, **kwargs): if DEBUG: print("#>",*args, **kwargs) if DEBUG: nk = "4 3" c = "1 3 2 8 5 5 8 2 2 8 5 2" f = "1 2 2 5" h = "2 6 7" else: nk = input() c = input() f = input() h = input() n, k = map(int, nk.split()) c = list(map(int, c.split())) f = list(map(int, f.split())) # n = len(f) # k = len(c) // n h = list(map(int, h.split())) znaki_s = set(c) # different card values in supply znaki_d = set(f) # different card values in demand znaki = set(c + f) # different card values in game # find supply and demand supply = {} demand = {} for z in znaki_s: supply[z] = c.count(z) for z in znaki_d: demand[z] = f.count(z) dprint("supply:", supply) dprint("demand:", demand) # build H-matrix dm = max(demand.values()) sm = max(supply.values()) dprint(znaki, sm, dm) if n == 4: print (21) elif n == 3: print (0) else: print (demand, f, h) ```
instruction
0
7,281
19
14,562
No
output
1
7,281
19
14,563
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice, Bob and Charlie are playing Card Game for Three, as below: * At first, each of the three players has a deck consisting of some number of cards. Alice's deck has N cards, Bob's deck has M cards, and Charlie's deck has K cards. Each card has a letter `a`, `b` or `c` written on it. The orders of the cards in the decks cannot be rearranged. * The players take turns. Alice goes first. * If the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says `a`, Alice takes the next turn.) * If the current player's deck is empty, the game ends and the current player wins the game. There are 3^{N+M+K} possible patters of the three player's initial decks. Among these patterns, how many will lead to Alice's victory? Since the answer can be large, print the count modulo 1\,000\,000\,007 (=10^9+7). Constraints * 1 \leq N \leq 3Γ—10^5 * 1 \leq M \leq 3Γ—10^5 * 1 \leq K \leq 3Γ—10^5 Input The input is given from Standard Input in the following format: N M K Output Print the answer modulo 1\,000\,000\,007 (=10^9+7). Examples Input 1 1 1 Output 17 Input 4 2 2 Output 1227 Input 1000 1000 1000 Output 261790852 Submitted Solution: ``` mod=int(1E9+7) JS=[1] for i in range(1,4000): JS.append(JS[-1]*i%mod) Cs=lambda x,y:js(x)*inv(js(y))*inv(js(x-y))%mod inv =lambda x:pow(x,mod-2,mod) js=lambda x:JS[x] #while True: A,B,C=map(int,input().split()) A-=1;B+=1;C+=1; ans=0 for x in range(1,B+1): for y in range(1,C+1): ans+=Cs(A+B-x+C-y,A)*Cs(B-x+C-y,B-x)*pow(3,x-1+y-1,mod)%mod ans%=mod print(ans) ```
instruction
0
7,418
19
14,836
No
output
1
7,418
19
14,837
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice, Bob and Charlie are playing Card Game for Three, as below: * At first, each of the three players has a deck consisting of some number of cards. Alice's deck has N cards, Bob's deck has M cards, and Charlie's deck has K cards. Each card has a letter `a`, `b` or `c` written on it. The orders of the cards in the decks cannot be rearranged. * The players take turns. Alice goes first. * If the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says `a`, Alice takes the next turn.) * If the current player's deck is empty, the game ends and the current player wins the game. There are 3^{N+M+K} possible patters of the three player's initial decks. Among these patterns, how many will lead to Alice's victory? Since the answer can be large, print the count modulo 1\,000\,000\,007 (=10^9+7). Constraints * 1 \leq N \leq 3Γ—10^5 * 1 \leq M \leq 3Γ—10^5 * 1 \leq K \leq 3Γ—10^5 Input The input is given from Standard Input in the following format: N M K Output Print the answer modulo 1\,000\,000\,007 (=10^9+7). Examples Input 1 1 1 Output 17 Input 4 2 2 Output 1227 Input 1000 1000 1000 Output 261790852 Submitted Solution: ``` #include <bits/stdc++.h> using namespace std; long long mod_pow(long long base, long long exp) { if (exp == 0) return 1; if (exp & 1) return (mod_pow(base, exp - 1) * base) % 1000000007; else return mod_pow((base * base) % 1000000007, exp / 2); } long long fac[3 * 1000 + 1]; long long fac_inv[3 * 1000 + 1]; long long C(long long n, long long k) { if (k < 0 || n < k) return 0; long long num = fac[n]; long long den = (fac_inv[n - k] * fac_inv[k]) % 1000000007; return (num * den) % 1000000007; } int main() { fac[0] = 1; for (long long n = 1; n <= 3 * 1000; n++) fac[n] = (fac[n - 1] * n) % 1000000007; fac_inv[3 * 1000] = mod_pow(fac[3 * 1000], 1000000007 - 2); for (long long n = 3 * 1000 - 1; n >= 0; n--) fac_inv[n] = (fac_inv[n + 1] * (n + 1)) % 1000000007; long long a, b, c; cin >> a >> b >> c; a++; if (!(b > c)) { b = b ^ c; c = b ^ c; b = b ^ c; } long long ans = 0; long long sum = 1; long long pull = 0; for (long long n = a; n <= a + b + c; n++) { long long sub = 0; sub = (sub + sum - pull) % 1000000007; sub = (sub * C(n - 2, a - 2)) % 1000000007; sub = (sub * mod_pow(3, a + b + c - n)) % 1000000007; ans = (ans + sub) % 1000000007; sum = (2 * sum - C(n - a, c)) % 1000000007; pull = (2 * pull + C(n - a, n - a - b)) % 1000000007; } cout << (ans + 1000000007) % 1000000007 << endl; return 0; } ```
instruction
0
7,419
19
14,838
No
output
1
7,419
19
14,839
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice, Bob and Charlie are playing Card Game for Three, as below: * At first, each of the three players has a deck consisting of some number of cards. Alice's deck has N cards, Bob's deck has M cards, and Charlie's deck has K cards. Each card has a letter `a`, `b` or `c` written on it. The orders of the cards in the decks cannot be rearranged. * The players take turns. Alice goes first. * If the current player's deck contains at least one card, discard the top card in the deck. Then, the player whose name begins with the letter on the discarded card, takes the next turn. (For example, if the card says `a`, Alice takes the next turn.) * If the current player's deck is empty, the game ends and the current player wins the game. There are 3^{N+M+K} possible patters of the three player's initial decks. Among these patterns, how many will lead to Alice's victory? Since the answer can be large, print the count modulo 1\,000\,000\,007 (=10^9+7). Constraints * 1 \leq N \leq 3Γ—10^5 * 1 \leq M \leq 3Γ—10^5 * 1 \leq K \leq 3Γ—10^5 Input The input is given from Standard Input in the following format: N M K Output Print the answer modulo 1\,000\,000\,007 (=10^9+7). Examples Input 1 1 1 Output 17 Input 4 2 2 Output 1227 Input 1000 1000 1000 Output 261790852 Submitted Solution: ``` mod=int(1E9+7) JS=[1] for i in range(1,5000): JS.append(JS[-1]*i%mod) Cs=lambda x,y:js(x)*inv(js(y))*inv(js(x-y))%mod inv =lambda x:pow(x,mod-2,mod) js=lambda x:JS[x] #while True: A,B,C=map(int,input().split()) A-=1;B+=1;C+=1; ans=0 for x in range(1,B+1): for y in range(1,C+1): ans+=Cs(A+B-x+C-y,A)*Cs(B-x+C-y,B-x)*pow(3,x-1+y-1,mod)%mod ans%=mod print(ans) ```
instruction
0
7,420
19
14,840
No
output
1
7,420
19
14,841
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,565
19
15,130
Tags: implementation Correct Solution: ``` # Blackjack def cards(n): diff = n - 10 if diff == 10: return 15 if diff > 11 or diff == 0: return 0 if n < 10: return 0 else: return 4 n = int(input()) print(cards(n)) ```
output
1
7,565
19
15,131
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,566
19
15,132
Tags: implementation Correct Solution: ``` n = int(input()) if 1 <= n-10 <= 9 or n-10 == 11: print("4") elif n-10 == 10: print("15") else: print("0") ```
output
1
7,566
19
15,133
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,567
19
15,134
Tags: implementation Correct Solution: ``` n = int(input()) if n <= 10 or n > 21: print(0) else: if n == 11 or n == 21: print(4) elif n - 10 < 10: print(4) else: print(15) ```
output
1
7,567
19
15,135
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,568
19
15,136
Tags: implementation Correct Solution: ``` n=int(input()) n=n-10 if(n>=1 and n<=9): print(4) elif(n==10): print(15) elif(n==11): print(4) else: print(0) ```
output
1
7,568
19
15,137
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,569
19
15,138
Tags: implementation Correct Solution: ``` n=int(input()) if 11<=n<=19: print(4) elif n==20: print(15) elif n==21: print(4) else: print(0) ```
output
1
7,569
19
15,139
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,570
19
15,140
Tags: implementation Correct Solution: ``` a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 10] * 4 a = a[:-1] def solve(n): print(a.count(n - 10)) n, = map(int, input().split()) solve(n) ```
output
1
7,570
19
15,141
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,571
19
15,142
Tags: implementation Correct Solution: ``` n=int(input()) x=n-10 if(x<=0): print(0) else: if(x>11): print(0) elif(x==10): print(15) else: print(4) ```
output
1
7,571
19
15,143
Provide tags and a correct Python 3 solution for this coding contest problem. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points.
instruction
0
7,572
19
15,144
Tags: implementation Correct Solution: ``` # import sys # sys.stdin=open("input.in",'r') # sys.stdout=open("out.out",'w') n=int(input())-10 if n<=0: print(0) elif n==10: print(15) elif n<12: print(4) else: print(0) ```
output
1
7,572
19
15,145
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` x = int(input())-10 if 1<=x<=9 or x == 11: print(4) elif x==10 or x==20: print(15) else: print(0) ```
instruction
0
7,573
19
15,146
Yes
output
1
7,573
19
15,147
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` """ *** Author--Saket Saumya *** IIITM """ import math from sys import stdin def si(): return str(input()) def ii(): return int(input()) def mi(): return map(int, input().split()) def li(): return list(mi()) n=ii() s=n-10 if s==0 or s>=12 or s<0: print('0') if(s==1) or s==2 or s==3 or s==4 or s==5 or s==6 or s==7 or s==8 or s==9: print('4') if(s==10): print('15') if s==11: print('4') ```
instruction
0
7,574
19
15,148
Yes
output
1
7,574
19
15,149
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` n = int(input()) if (n >= 0 and n <= 10) or n >= 22: print(0) elif (n >= 11 and n < 20) or n == 21: print(4) elif n == 20: print(15) ```
instruction
0
7,575
19
15,150
Yes
output
1
7,575
19
15,151
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` n=int(input()) if (n-10)<=0 or n>=22: print(0) elif 1<=(n-10)<=11 and n!=20: print(4) elif n==20: print(15) ```
instruction
0
7,576
19
15,152
Yes
output
1
7,576
19
15,153
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` n=int(input()) if n==10: print('0') elif n==20: print('15') else: print('4') ```
instruction
0
7,577
19
15,154
No
output
1
7,577
19
15,155
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` n=int(input()) if(n<=10): print('0') else: t=n-10 if(t==10): print('15') else: print('4') ```
instruction
0
7,578
19
15,156
No
output
1
7,578
19
15,157
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` def ans(n): if(n==0 or n>11): return 0 elif(1<=n<10) or (n==11): return 4 else: return 15 n=int(input()) n-=10 print(ans(n)) ```
instruction
0
7,579
19
15,158
No
output
1
7,579
19
15,159
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one! Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture. In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses. The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n. Input The only line contains n (1 ≀ n ≀ 25) β€” the required sum of points. Output Print the numbers of ways to get the second card in the required way if the first card is the queen of spades. Examples Input 12 Output 4 Input 20 Output 15 Input 10 Output 0 Note In the first sample only four two's of different suits can earn the required sum of points. In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use. In the third sample there is no card, that would add a zero to the current ten points. Submitted Solution: ``` n = int(input()) if n == 20: print(15) elif 10 < n < 22: print(0) else: print(4) ```
instruction
0
7,580
19
15,160
No
output
1
7,580
19
15,161
Provide tags and a correct Python 3 solution for this coding contest problem. Gildong is developing a game consisting of n stages numbered from 1 to n. The player starts the game from the 1-st stage and should beat the stages in increasing order of the stage number. The player wins the game after beating the n-th stage. There is at most one checkpoint on each stage, and there is always a checkpoint on the 1-st stage. At the beginning of the game, only the checkpoint on the 1-st stage is activated, and all other checkpoints are deactivated. When the player gets to the i-th stage that has a checkpoint, that checkpoint is activated. For each try of a stage, the player can either beat the stage or fail the stage. If they beat the i-th stage, the player is moved to the i+1-st stage. If they fail the i-th stage, the player is moved to the most recent checkpoint they activated, and they have to beat the stages after that checkpoint again. For example, assume that n = 4 and the checkpoints are on the 1-st and 3-rd stages. The player starts at the 1-st stage. If they fail on the 1-st stage, they need to retry the 1-st stage because the checkpoint on the 1-st stage is the most recent checkpoint they activated. If the player beats the 1-st stage, they're moved to the 2-nd stage. If they fail it, they're sent back to the 1-st stage again. If they beat both the 1-st stage and the 2-nd stage, they get to the 3-rd stage and the checkpoint on the 3-rd stage is activated. Now whenever they fail on the 3-rd stage, or the 4-th stage after beating the 3-rd stage, they're sent back to the 3-rd stage. If they beat both the 3-rd stage and the 4-th stage, they win the game. Gildong is going to build the stages to have equal difficulty. He wants you to find any series of stages and checkpoints using at most 2000 stages, where the [expected number](https://en.wikipedia.org/wiki/Expected_value) of tries over all stages is exactly k, for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Input Each test contains one or more test cases. The first line contains the number of test cases t (1 ≀ t ≀ 50). Each test case contains exactly one line. The line consists of a single integer k (1 ≀ k ≀ 10^{18}) β€” the expected number of tries over all stages Gildong wants to set for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Output For each test case, print -1 if it's impossible to construct such a series of stages and checkpoints using at most 2000 stages. Otherwise, print two lines. The first line should contain a single integer n (1 ≀ n ≀ 2000) – the number of stages. The second line should contain n integers, where the i-th integer represents whether the i-th stage has a checkpoint. The i-th integer should be 0 if the i-th stage doesn't have a checkpoint, and 1 if it has a checkpoint. Note that the first integer must be 1 according to the description. Example Input 4 1 2 8 12 Output -1 1 1 4 1 1 1 1 5 1 1 0 1 1 Note In the first and the second case, we can see that the 'easiest' series of stages is to have 1 stage with a checkpoint. This already requires 2 tries in expectation, so it is impossible to make it to require only 1 try. In the third case, it takes 2 tries in expectation to beat each stage, and the player can always retry that stage without falling back to one of the previous stages if they fail it. Therefore the total expected number of tries is 8. Note that there exists an answer with fewer stages, but you are not required to minimize the number of stages used.
instruction
0
7,767
19
15,534
Tags: brute force, constructive algorithms, greedy, math, probabilities Correct Solution: ``` for _ in range(int(input())): n = int(input()) a = [] if n % 2 == 1: print(-1) continue if n <= 4000: print(n // 2) print('1 ' * (n // 2)) continue while n > 0: a.append(1) n -= 2 s = 2 while n > s * 2: a.append(0) s *= 2 n -= s if len(a) <= 2000: print(len(a)) print(*a, end=' ') else: print(-1) ```
output
1
7,767
19
15,535
Provide tags and a correct Python 3 solution for this coding contest problem. Gildong is developing a game consisting of n stages numbered from 1 to n. The player starts the game from the 1-st stage and should beat the stages in increasing order of the stage number. The player wins the game after beating the n-th stage. There is at most one checkpoint on each stage, and there is always a checkpoint on the 1-st stage. At the beginning of the game, only the checkpoint on the 1-st stage is activated, and all other checkpoints are deactivated. When the player gets to the i-th stage that has a checkpoint, that checkpoint is activated. For each try of a stage, the player can either beat the stage or fail the stage. If they beat the i-th stage, the player is moved to the i+1-st stage. If they fail the i-th stage, the player is moved to the most recent checkpoint they activated, and they have to beat the stages after that checkpoint again. For example, assume that n = 4 and the checkpoints are on the 1-st and 3-rd stages. The player starts at the 1-st stage. If they fail on the 1-st stage, they need to retry the 1-st stage because the checkpoint on the 1-st stage is the most recent checkpoint they activated. If the player beats the 1-st stage, they're moved to the 2-nd stage. If they fail it, they're sent back to the 1-st stage again. If they beat both the 1-st stage and the 2-nd stage, they get to the 3-rd stage and the checkpoint on the 3-rd stage is activated. Now whenever they fail on the 3-rd stage, or the 4-th stage after beating the 3-rd stage, they're sent back to the 3-rd stage. If they beat both the 3-rd stage and the 4-th stage, they win the game. Gildong is going to build the stages to have equal difficulty. He wants you to find any series of stages and checkpoints using at most 2000 stages, where the [expected number](https://en.wikipedia.org/wiki/Expected_value) of tries over all stages is exactly k, for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Input Each test contains one or more test cases. The first line contains the number of test cases t (1 ≀ t ≀ 50). Each test case contains exactly one line. The line consists of a single integer k (1 ≀ k ≀ 10^{18}) β€” the expected number of tries over all stages Gildong wants to set for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Output For each test case, print -1 if it's impossible to construct such a series of stages and checkpoints using at most 2000 stages. Otherwise, print two lines. The first line should contain a single integer n (1 ≀ n ≀ 2000) – the number of stages. The second line should contain n integers, where the i-th integer represents whether the i-th stage has a checkpoint. The i-th integer should be 0 if the i-th stage doesn't have a checkpoint, and 1 if it has a checkpoint. Note that the first integer must be 1 according to the description. Example Input 4 1 2 8 12 Output -1 1 1 4 1 1 1 1 5 1 1 0 1 1 Note In the first and the second case, we can see that the 'easiest' series of stages is to have 1 stage with a checkpoint. This already requires 2 tries in expectation, so it is impossible to make it to require only 1 try. In the third case, it takes 2 tries in expectation to beat each stage, and the player can always retry that stage without falling back to one of the previous stages if they fail it. Therefore the total expected number of tries is 8. Note that there exists an answer with fewer stages, but you are not required to minimize the number of stages used.
instruction
0
7,768
19
15,536
Tags: brute force, constructive algorithms, greedy, math, probabilities Correct Solution: ``` # ------------------- fast io -------------------- import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------- fast io -------------------- from bisect import bisect_left as bsl powers=[2] for s in range(60): powers.append(powers[-1]*2) newy=[powers[0]] for s in range(1,len(powers)): newy.append(newy[-1]+powers[s]) if newy[-1]>=10**18: break for j in range(int(input())): k=int(input()) if k%2==1: print(-1) else: binrep=k-2 #see if we can construct k-2 using newy ans=[1] while binrep>0: ind=min(bsl(newy,binrep),len(newy)-1) if newy[ind]>binrep: ind-=1 for i in range(ind): ans.append(0) ans.append(1) binrep-=newy[ind] print(len(ans)) print(*ans) ```
output
1
7,768
19
15,537
Provide tags and a correct Python 3 solution for this coding contest problem. Gildong is developing a game consisting of n stages numbered from 1 to n. The player starts the game from the 1-st stage and should beat the stages in increasing order of the stage number. The player wins the game after beating the n-th stage. There is at most one checkpoint on each stage, and there is always a checkpoint on the 1-st stage. At the beginning of the game, only the checkpoint on the 1-st stage is activated, and all other checkpoints are deactivated. When the player gets to the i-th stage that has a checkpoint, that checkpoint is activated. For each try of a stage, the player can either beat the stage or fail the stage. If they beat the i-th stage, the player is moved to the i+1-st stage. If they fail the i-th stage, the player is moved to the most recent checkpoint they activated, and they have to beat the stages after that checkpoint again. For example, assume that n = 4 and the checkpoints are on the 1-st and 3-rd stages. The player starts at the 1-st stage. If they fail on the 1-st stage, they need to retry the 1-st stage because the checkpoint on the 1-st stage is the most recent checkpoint they activated. If the player beats the 1-st stage, they're moved to the 2-nd stage. If they fail it, they're sent back to the 1-st stage again. If they beat both the 1-st stage and the 2-nd stage, they get to the 3-rd stage and the checkpoint on the 3-rd stage is activated. Now whenever they fail on the 3-rd stage, or the 4-th stage after beating the 3-rd stage, they're sent back to the 3-rd stage. If they beat both the 3-rd stage and the 4-th stage, they win the game. Gildong is going to build the stages to have equal difficulty. He wants you to find any series of stages and checkpoints using at most 2000 stages, where the [expected number](https://en.wikipedia.org/wiki/Expected_value) of tries over all stages is exactly k, for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Input Each test contains one or more test cases. The first line contains the number of test cases t (1 ≀ t ≀ 50). Each test case contains exactly one line. The line consists of a single integer k (1 ≀ k ≀ 10^{18}) β€” the expected number of tries over all stages Gildong wants to set for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Output For each test case, print -1 if it's impossible to construct such a series of stages and checkpoints using at most 2000 stages. Otherwise, print two lines. The first line should contain a single integer n (1 ≀ n ≀ 2000) – the number of stages. The second line should contain n integers, where the i-th integer represents whether the i-th stage has a checkpoint. The i-th integer should be 0 if the i-th stage doesn't have a checkpoint, and 1 if it has a checkpoint. Note that the first integer must be 1 according to the description. Example Input 4 1 2 8 12 Output -1 1 1 4 1 1 1 1 5 1 1 0 1 1 Note In the first and the second case, we can see that the 'easiest' series of stages is to have 1 stage with a checkpoint. This already requires 2 tries in expectation, so it is impossible to make it to require only 1 try. In the third case, it takes 2 tries in expectation to beat each stage, and the player can always retry that stage without falling back to one of the previous stages if they fail it. Therefore the total expected number of tries is 8. Note that there exists an answer with fewer stages, but you are not required to minimize the number of stages used.
instruction
0
7,769
19
15,538
Tags: brute force, constructive algorithms, greedy, math, probabilities Correct Solution: ``` from sys import stdin input = stdin.readline for _ in range(int(input())): n = int(input()) s = '' if n % 2: print(-1) continue n //= 2 a = bin(n)[2:] n = len(a) for x in range(n - 1, 0, -1): if a[n - 1 - x] == '0': continue s += '1 ' + '0 ' * (x - 1) + '1 ' if a[n - 1] == '1': s += '1 ' print(len(s) // 2) print(s) ```
output
1
7,769
19
15,539
Provide tags and a correct Python 3 solution for this coding contest problem. Gildong is developing a game consisting of n stages numbered from 1 to n. The player starts the game from the 1-st stage and should beat the stages in increasing order of the stage number. The player wins the game after beating the n-th stage. There is at most one checkpoint on each stage, and there is always a checkpoint on the 1-st stage. At the beginning of the game, only the checkpoint on the 1-st stage is activated, and all other checkpoints are deactivated. When the player gets to the i-th stage that has a checkpoint, that checkpoint is activated. For each try of a stage, the player can either beat the stage or fail the stage. If they beat the i-th stage, the player is moved to the i+1-st stage. If they fail the i-th stage, the player is moved to the most recent checkpoint they activated, and they have to beat the stages after that checkpoint again. For example, assume that n = 4 and the checkpoints are on the 1-st and 3-rd stages. The player starts at the 1-st stage. If they fail on the 1-st stage, they need to retry the 1-st stage because the checkpoint on the 1-st stage is the most recent checkpoint they activated. If the player beats the 1-st stage, they're moved to the 2-nd stage. If they fail it, they're sent back to the 1-st stage again. If they beat both the 1-st stage and the 2-nd stage, they get to the 3-rd stage and the checkpoint on the 3-rd stage is activated. Now whenever they fail on the 3-rd stage, or the 4-th stage after beating the 3-rd stage, they're sent back to the 3-rd stage. If they beat both the 3-rd stage and the 4-th stage, they win the game. Gildong is going to build the stages to have equal difficulty. He wants you to find any series of stages and checkpoints using at most 2000 stages, where the [expected number](https://en.wikipedia.org/wiki/Expected_value) of tries over all stages is exactly k, for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Input Each test contains one or more test cases. The first line contains the number of test cases t (1 ≀ t ≀ 50). Each test case contains exactly one line. The line consists of a single integer k (1 ≀ k ≀ 10^{18}) β€” the expected number of tries over all stages Gildong wants to set for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Output For each test case, print -1 if it's impossible to construct such a series of stages and checkpoints using at most 2000 stages. Otherwise, print two lines. The first line should contain a single integer n (1 ≀ n ≀ 2000) – the number of stages. The second line should contain n integers, where the i-th integer represents whether the i-th stage has a checkpoint. The i-th integer should be 0 if the i-th stage doesn't have a checkpoint, and 1 if it has a checkpoint. Note that the first integer must be 1 according to the description. Example Input 4 1 2 8 12 Output -1 1 1 4 1 1 1 1 5 1 1 0 1 1 Note In the first and the second case, we can see that the 'easiest' series of stages is to have 1 stage with a checkpoint. This already requires 2 tries in expectation, so it is impossible to make it to require only 1 try. In the third case, it takes 2 tries in expectation to beat each stage, and the player can always retry that stage without falling back to one of the previous stages if they fail it. Therefore the total expected number of tries is 8. Note that there exists an answer with fewer stages, but you are not required to minimize the number of stages used.
instruction
0
7,770
19
15,540
Tags: brute force, constructive algorithms, greedy, math, probabilities Correct Solution: ``` def read_int(): return int(input()) def read_ints(): return map(int, input().split(' ')) t = read_int() a = [2] while a[-1] < 1e18: a.append(a[-1] * 2 + 2) for case_num in range(t): n = read_int() if n % 2 == 1: print(-1) continue ans = [] pos = len(a) - 1 while n > 0: while a[pos] > n: pos -= 1 n -= a[pos] ans += [1] + ([0] * pos) print(len(ans)) print(' '.join(map(str, ans))) ```
output
1
7,770
19
15,541
Provide tags and a correct Python 3 solution for this coding contest problem. Gildong is developing a game consisting of n stages numbered from 1 to n. The player starts the game from the 1-st stage and should beat the stages in increasing order of the stage number. The player wins the game after beating the n-th stage. There is at most one checkpoint on each stage, and there is always a checkpoint on the 1-st stage. At the beginning of the game, only the checkpoint on the 1-st stage is activated, and all other checkpoints are deactivated. When the player gets to the i-th stage that has a checkpoint, that checkpoint is activated. For each try of a stage, the player can either beat the stage or fail the stage. If they beat the i-th stage, the player is moved to the i+1-st stage. If they fail the i-th stage, the player is moved to the most recent checkpoint they activated, and they have to beat the stages after that checkpoint again. For example, assume that n = 4 and the checkpoints are on the 1-st and 3-rd stages. The player starts at the 1-st stage. If they fail on the 1-st stage, they need to retry the 1-st stage because the checkpoint on the 1-st stage is the most recent checkpoint they activated. If the player beats the 1-st stage, they're moved to the 2-nd stage. If they fail it, they're sent back to the 1-st stage again. If they beat both the 1-st stage and the 2-nd stage, they get to the 3-rd stage and the checkpoint on the 3-rd stage is activated. Now whenever they fail on the 3-rd stage, or the 4-th stage after beating the 3-rd stage, they're sent back to the 3-rd stage. If they beat both the 3-rd stage and the 4-th stage, they win the game. Gildong is going to build the stages to have equal difficulty. He wants you to find any series of stages and checkpoints using at most 2000 stages, where the [expected number](https://en.wikipedia.org/wiki/Expected_value) of tries over all stages is exactly k, for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Input Each test contains one or more test cases. The first line contains the number of test cases t (1 ≀ t ≀ 50). Each test case contains exactly one line. The line consists of a single integer k (1 ≀ k ≀ 10^{18}) β€” the expected number of tries over all stages Gildong wants to set for a player whose probability of beating each stage is exactly \cfrac{1}{2}. Output For each test case, print -1 if it's impossible to construct such a series of stages and checkpoints using at most 2000 stages. Otherwise, print two lines. The first line should contain a single integer n (1 ≀ n ≀ 2000) – the number of stages. The second line should contain n integers, where the i-th integer represents whether the i-th stage has a checkpoint. The i-th integer should be 0 if the i-th stage doesn't have a checkpoint, and 1 if it has a checkpoint. Note that the first integer must be 1 according to the description. Example Input 4 1 2 8 12 Output -1 1 1 4 1 1 1 1 5 1 1 0 1 1 Note In the first and the second case, we can see that the 'easiest' series of stages is to have 1 stage with a checkpoint. This already requires 2 tries in expectation, so it is impossible to make it to require only 1 try. In the third case, it takes 2 tries in expectation to beat each stage, and the player can always retry that stage without falling back to one of the previous stages if they fail it. Therefore the total expected number of tries is 8. Note that there exists an answer with fewer stages, but you are not required to minimize the number of stages used.
instruction
0
7,771
19
15,542
Tags: brute force, constructive algorithms, greedy, math, probabilities Correct Solution: ``` t = int(input()) al = [2] for i in range(100): al.append(al[-1] * 2 + 2) #print(al) for q in range(t): k = int(input()) if k % 2 == 1: print(-1) else: mas = [] while k > 0: y = 0 while al[y] <= k: y += 1 y -= 1 mas.append(y) k -= al[y] z = 0 for i in mas: z += i + 1 print(z) for i in mas: print(1, end = ' ') for j in range(i): print(0, end = ' ') print() ```
output
1
7,771
19
15,543