text stringlengths 198 433k | conversation_id int64 0 109k |
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
MOD = 998244353
ROOT = 3
class Convolution_998244353():
def __init__(self):
self.first1 = True
self.first2 = True
self.sum_e = [0] * 30
self.sum_ie = [0] * 30
def inv_gcd(self, a, b):
a %= b
if a == 0: return b, 0
s = b
t = a
m0 = 0
m1 = 1
while t:
u = s // t
s -= t * u
m0 -= m1 * u
s, t = t, s
m0, m1 = m1, m0
if m0 < 0: m0 += b // s
return s, m0
def butterfly(self, arr):
n = len(arr)
h = (n - 1).bit_length()
if self.first1:
self.first1 = False
es = [0] * 30
ies = [0] * 30
m = MOD - 1
cnt2 = (m & -m).bit_length() - 1
e = pow(ROOT, m >> cnt2, MOD)
ie = pow(e, MOD - 2, MOD)
for i in range(cnt2 - 1)[::-1]:
es[i] = e
ies[i] = ie
e *= e
e %= MOD
ie *= ie
ie %= MOD
now = 1
for i in range(cnt2 - 2):
self.sum_e[i] = es[i] * now % MOD
now *= ies[i]
now %= MOD
for ph in range(1, h + 1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
now = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p] * now
arr[i + offset] = (l + r) % MOD
arr[i + offset + p] = (l - r) % MOD
now *= self.sum_e[(~s & -~s).bit_length() - 1]
now %= MOD
def butterfly_inv(self, arr):
n = len(arr)
h = (n - 1).bit_length()
if self.first2:
self.first2 = False
es = [0] * 30
ies = [0] * 30
m = MOD - 1
cnt2 = (m & -m).bit_length() - 1
e = pow(ROOT, m >> cnt2, MOD)
ie = pow(e, MOD - 2, MOD)
for i in range(cnt2 - 1)[::-1]:
es[i] = e
ies[i] = ie
e *= e
e %= MOD
ie *= ie
ie %= MOD
now = 1
for i in range(cnt2 - 2):
self.sum_ie[i] = ies[i] * now % MOD
now *= es[i]
now %= MOD
for ph in range(1, h + 1)[::-1]:
w = 1 << (ph - 1)
p = 1 << (h - ph)
inow = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p]
arr[i + offset] = (l + r) % MOD
arr[i + offset + p] = (MOD + l - r) * inow % MOD
inow *= self.sum_ie[(~s & -~s).bit_length() - 1]
inow %= MOD
def convolution(self, a, b):
n = len(a)
m = len(b)
if not n or not m: return []
if min(n, m) <= 50:
if n < m:
n, m = m, n
a, b = b, a
res = [0] * (n + m - 1)
for i in range(n):
for j in range(m):
res[i + j] += a[i] * b[j]
res[i + j] %= MOD
return res
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
self.butterfly(a)
self.butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD
self.butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, MOD - 2, MOD)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= MOD
return a
def autocorrelation(self, a):
n = len(a)
if not n: return []
if n <= 50:
res = [0] * (2 * n - 1)
for i in range(n):
for j in range(n):
res[i + j] += a[i] * a[j]
res[i + j] %= MOD
return res
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
self.butterfly(a)
for i in range(a):
a[i] *= a[i]
a[i] %= MOD
self.butterfly_inv(a)
a = a[:2 * n - 1]
iz = pow(z, MOD - 2, MOD)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= MOD
return a
import sys
input = sys.stdin.buffer.readline
N, M = map(int, input().split())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]
cv = Convolution_998244353()
print(*cv.convolution(A, B))
```
Yes
| 97,600 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
#!usr/bin/env python3
from collections import defaultdict, deque, Counter, OrderedDict
from bisect import bisect_left, bisect_right
from functools import reduce, lru_cache
from heapq import heappush, heappop, heapify
import itertools
import math, fractions
import sys, copy
def L(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline().rstrip())
def SL(): return list(sys.stdin.readline().rstrip())
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI1(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LS(): return [list(x) for x in sys.stdin.readline().split()]
def R(n): return [sys.stdin.readline().strip() for _ in range(n)]
def LR(n): return [L() for _ in range(n)]
def IR(n): return [I() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def LIR1(n): return [LI1() for _ in range(n)]
def SR(n): return [SL() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
def perm(n, r): return math.factorial(n) // math.factorial(r)
def comb(n, r): return math.factorial(n) // (math.factorial(r) * math.factorial(n-r))
def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if len(args) > 0 else [default for _ in range(n)]
dire = [[1, 0], [0, 1], [-1, 0], [0, -1]]
dire8 = [[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]
alphabets = "abcdefghijklmnopqrstuvwxyz"
ALPHABETS = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
MOD = 1000000007
INF = float("inf")
sys.setrecursionlimit(1000000)
class NTT:
'''
conv: ci = ∑_{j=0}^i a_j * b_{i−j} % mod
添字の和がiになるajとbkの積の和
'''
def __init__(self, a, b, mod=998244353, root=3):
self.mod, self.root = mod, root
deg = len(a) + len(b) - 2
self.n = deg.bit_length()
N = 1 << self.n
self.roots = [pow(self.root, (self.mod-1)>>i, self.mod) for i in range(24)] # 1 の 2^i 乗根
self.iroots = [pow(x,self.mod-2,self.mod) for x in self.roots] # 1 の 2^i 乗根の逆元
self.conv = a + [0]*(N-len(a))
self.b = b + [0]*(N-len(b))
self.untt()
self.untt(False)
for i in range(N):
self.conv[i] = self.conv[i] * self.b[i] % self.mod
self.iuntt()
del self.conv[deg+1:] # inplace ver. of self.conv[:deg+1]
def untt(self, flag=True):
a = self.conv if flag else self.b
for i in range(self.n):
m = 1 << (self.n - i - 1)
for s in range(1 << i):
W = 1
s *= m * 2
for p in range(m):
a[s+p], a[s+p+m] = (a[s+p]+a[s+p+m]) % self.mod, (a[s+p]-a[s+p+m]) * W % self.mod
W = W * self.roots[self.n-i] % self.mod
def iuntt(self):
for i in range(self.n):
m = 1 << i
for s in range(1 << (self.n-i-1)):
W = 1
s *= m * 2
for p in range(m):
self.conv[s+p], self.conv[s+p+m] = (self.conv[s+p]+self.conv[s+p+m]*W)%self.mod, (self.conv[s+p]-self.conv[s+p+m]*W)%self.mod
W = W * self.iroots[i+1] % self.mod
inv = pow((self.mod + 1) // 2, self.n, self.mod)
for i in range(1<<self.n):
self.conv[i] = self.conv[i] * inv % self.mod
def main():
N, M = LI()
a = LI()
b = LI()
ntt = NTT(a, b)
print(*ntt.conv)
if __name__ == '__main__':
main()
```
Yes
| 97,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
MOD = 998244353
PROOT = 3
IPROOT = 665496235
roots = [pow(PROOT,(MOD-1)>>i,MOD) for i in range(24)] # 1 の 2^i 乗根
iroots = [pow(IPROOT,(MOD-1)>>i,MOD) for i in range(24)] # 1 の 2^i 乗根の逆元
def fft_stockham(A,n,inv=False):
N = 1<<n
for i in range(n):
nA = [0]*N
a = 1<<i
b = 1<<(n-i-1)
wb = iroots[i+1] if inv else roots[i+1]
for j in range(b):
w = 1
for k in range(a):
nA[2*a*j+k] = (A[a*j+k] + A[a*j+N//2+k]*w)%MOD
nA[2*a*j+k+a] = (A[a*j+k] - A[a*j+N//2+k]*w)%MOD
w = w*wb%MOD
A = nA
return A
def convolution(a,b):
deg = len(a) + len(b) - 2
n = deg.bit_length()
N = 1<<n
a += [0]*(N-len(a))
b += [0]*(N-len(b))
fa = fft_stockham(a,n)
fb = fft_stockham(b,n)
inv = pow(1<<n,MOD-2,MOD)
for i in range(N):
fa[i] = fa[i]*fb[i]%MOD*inv%MOD
ab = fft_stockham(fa,n,True)
return ab[:deg+1]
n,m = map(int,input().split())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = convolution(a,b)
print(*c)
```
Yes
| 97,602 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
import sys
input = sys.stdin.readline
N, M = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
mod = 998244353
class FastModuloTransformation:
def __init__(self, n):
self.n = n
self.P = 998244353
self.g = 3
self.omega = pow(self.g, (self.P - 1) // n, self.P)
def bitrev(self, a):
n = self.n
x = n.bit_length() - 1
res = a[: ]
for i in range(n):
j = 0
for k in range(x): j |= (i & (1 << k) > 0) << (x - k - 1)
if i < j: res[i], res[j] = res[j], res[i]
return res
def fmt(self, a, base):
if n == 1: return a
P = self.P
omega = base
A = self.bitrev(a)
half = pow(omega, n >> 1, P)
i = n
m = 1
while i > 1:
i >>= 1
w = pow(omega, i, P)
wk = 1
for j in range(m):
for x in range(j, len(a), 2 * m):
l = A[x]
r = wk * A[x + m] % P
A[x] = (l + r) % P
A[x + m] = (l + r * half) % P
wk *= w
wk %= P
m <<= 1
return A
def ifmt(self, A):
if self.n == 1: return A
P = self.P
nrev = pow(self.n, P - 2, P)
return [(x * nrev) % P for x in self.fmt(A, pow(self.omega, P - 2, P))]
n = 1 << ((max(len(a), len(b))).bit_length()) + 1
fmt = FastModuloTransformation(n)
a = [0] * (n - N) + a
b = [0] * (n - M) + b
A = fmt.fmt(a, fmt.omega)
B = fmt.fmt(b, fmt.omega)
AB = [A[i] * B[i] % mod for i in range(n)]
ab = fmt.ifmt(AB)
print(*ab[-(N + M): -1])
```
No
| 97,603 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
import types
_atcoder_code = """
# Python port of AtCoder Library.
__version__ = '0.0.1'
"""
atcoder = types.ModuleType('atcoder')
exec(_atcoder_code, atcoder.__dict__)
_atcoder__bit_code = """
def _ceil_pow2(n: int) -> int:
x = 0
while (1 << x) < n:
x += 1
return x
def _bsf(n: int) -> int:
x = 0
while n % 2 == 0:
x += 1
n //= 2
return x
"""
atcoder._bit = types.ModuleType('atcoder._bit')
exec(_atcoder__bit_code, atcoder._bit.__dict__)
_atcoder__math_code = """
import typing
def _is_prime(n: int) -> bool:
'''
Reference:
M. Forisek and J. Jancina,
Fast Primality Testing for Integers That Fit into a Machine Word
'''
if n <= 1:
return False
if n == 2 or n == 7 or n == 61:
return True
if n % 2 == 0:
return False
d = n - 1
while d % 2 == 0:
d //= 2
for a in (2, 7, 61):
t = d
y = pow(a, t, n)
while t != n - 1 and y != 1 and y != n - 1:
y = y * y % n
t <<= 1
if y != n - 1 and t % 2 == 0:
return False
return True
def _inv_gcd(a: int, b: int) -> typing.Tuple[int, int]:
a %= b
if a == 0:
return (b, 0)
# Contracts:
# [1] s - m0 * a = 0 (mod b)
# [2] t - m1 * a = 0 (mod b)
# [3] s * |m1| + t * |m0| <= b
s = b
t = a
m0 = 0
m1 = 1
while t:
u = s // t
s -= t * u
m0 -= m1 * u # |m1 * u| <= |m1| * s <= b
# [3]:
# (s - t * u) * |m1| + t * |m0 - m1 * u|
# <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
# = s * |m1| + t * |m0| <= b
s, t = t, s
m0, m1 = m1, m0
# by [3]: |m0| <= b/g
# by g != b: |m0| < b/g
if m0 < 0:
m0 += b // s
return (s, m0)
def _primitive_root(m: int) -> int:
if m == 2:
return 1
if m == 167772161:
return 3
if m == 469762049:
return 3
if m == 754974721:
return 11
if m == 998244353:
return 3
divs = [2] + [0] * 19
cnt = 1
x = (m - 1) // 2
while x % 2 == 0:
x //= 2
i = 3
while i * i <= x:
if x % i == 0:
divs[cnt] = i
cnt += 1
while x % i == 0:
x //= i
i += 2
if x > 1:
divs[cnt] = x
cnt += 1
g = 2
while True:
for i in range(cnt):
if pow(g, (m - 1) // divs[i], m) == 1:
break
else:
return g
g += 1
"""
atcoder._math = types.ModuleType('atcoder._math')
exec(_atcoder__math_code, atcoder._math.__dict__)
_atcoder_modint_code = """
from __future__ import annotations
import typing
# import atcoder._math
class ModContext:
context = []
def __init__(self, mod: int) -> None:
assert 1 <= mod
self.mod = mod
def __enter__(self) -> None:
self.context.append(self.mod)
def __exit__(self, exc_type: typing.Any, exc_value: typing.Any,
traceback: typing.Any) -> None:
self.context.pop()
@classmethod
def get_mod(cls) -> int:
return cls.context[-1]
class Modint:
def __init__(self, v: int = 0) -> None:
self._mod = ModContext.get_mod()
if v == 0:
self._v = 0
else:
self._v = v % self._mod
def val(self) -> int:
return self._v
def __iadd__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
self._v += rhs._v
else:
self._v += rhs
if self._v >= self._mod:
self._v -= self._mod
return self
def __isub__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
self._v -= rhs._v
else:
self._v -= rhs
if self._v < 0:
self._v += self._mod
return self
def __imul__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
self._v = self._v * rhs._v % self._mod
else:
self._v = self._v * rhs % self._mod
return self
def __ifloordiv__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
inv = rhs.inv()._v
else:
inv = atcoder._math._inv_gcd(rhs, self._mod)[1]
self._v = self._v * inv % self._mod
return self
def __pos__(self) -> Modint:
return self
def __neg__(self) -> Modint:
return Modint() - self
def __pow__(self, n: int) -> Modint:
assert 0 <= n
return Modint(pow(self._v, n, self._mod))
def inv(self) -> Modint:
eg = atcoder._math._inv_gcd(self._v, self._mod)
assert eg[0] == 1
return Modint(eg[1])
def __add__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
result = self._v + rhs._v
if result >= self._mod:
result -= self._mod
return raw(result)
else:
return Modint(self._v + rhs)
def __sub__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
result = self._v - rhs._v
if result < 0:
result += self._mod
return raw(result)
else:
return Modint(self._v - rhs)
def __mul__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
return Modint(self._v * rhs._v)
else:
return Modint(self._v * rhs)
def __floordiv__(self, rhs: typing.Union[Modint, int]) -> Modint:
if isinstance(rhs, Modint):
inv = rhs.inv()._v
else:
inv = atcoder._math._inv_gcd(rhs, self._mod)[1]
return Modint(self._v * inv)
def __eq__(self, rhs: typing.Union[Modint, int]) -> bool:
if isinstance(rhs, Modint):
return self._v == rhs._v
else:
return self._v == rhs
def __ne__(self, rhs: typing.Union[Modint, int]) -> bool:
if isinstance(rhs, Modint):
return self._v != rhs._v
else:
return self._v != rhs
def raw(v: int) -> Modint:
x = Modint()
x._v = v
return x
"""
atcoder.modint = types.ModuleType('atcoder.modint')
atcoder.modint.__dict__['atcoder'] = atcoder
atcoder.modint.__dict__['atcoder._math'] = atcoder._math
exec(_atcoder_modint_code, atcoder.modint.__dict__)
ModContext = atcoder.modint.ModContext
Modint = atcoder.modint.Modint
_atcoder_convolution_code = """
import typing
# import atcoder._bit
# import atcoder._math
# from atcoder.modint import ModContext, Modint
_sum_e = {} # _sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
def _butterfly(a: typing.List[Modint]) -> None:
g = atcoder._math._primitive_root(a[0].mod())
n = len(a)
h = atcoder._bit._ceil_pow2(n)
if a[0].mod() not in _sum_e:
es = [0] * 30 # es[i]^(2^(2+i)) == 1
ies = [0] * 30
cnt2 = atcoder._bit._bsf(a[0].mod() - 1)
e = Modint(g).pow((a[0].mod() - 1) >> cnt2)
ie = e.inv()
for i in range(cnt2, 1, -1):
# e^(2^i) == 1
es[i - 2] = e
ies[i - 2] = ie
e *= e
ie *= ie
sum_e = [0] * 30
now = Modint(1)
for i in range(cnt2 - 2):
sum_e[i] = es[i] * now
now *= ies[i]
_sum_e[a[0].mod()] = sum_e
else:
sum_e = _sum_e[a[0].mod()]
for ph in (1, h + 1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
now = Modint(1)
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
left = a[i + offset]
right = a[i + offset + p] * now
a[i + offset] = left + right
a[i + offset + p] = left - right
now *= sum_e[atcoder._bit._bsf(~s)]
_sum_ie = {} # _sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
def _butterfly_inv(a: typing.List[Modint]) -> None:
g = atcoder._math._primitive_root(a[0].mod())
n = len(a)
h = atcoder._bit.ceil_pow2(n)
if a[0].mod() not in _sum_ie:
es = [0] * 30 # es[i]^(2^(2+i)) == 1
ies = [0] * 30
cnt2 = atcoder._bit._bsf(a[0].mod() - 1)
e = Modint(g).pow((a[0].mod() - 1) >> cnt2)
ie = e.inv()
for i in range(cnt2, 1, -1):
# e^(2^i) == 1
es[i - 2] = e
ies[i - 2] = ie
e *= e
ie *= ie
sum_ie = [0] * 30
now = Modint(1)
for i in range(cnt2 - 2):
sum_ie[i] = ies[i] * now
now *= es[i]
_sum_ie[a[0].mod()] = sum_ie
else:
sum_ie = _sum_ie[a[0].mod()]
for ph in range(h, 0, -1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
inow = Modint(1)
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
left = a[i + offset]
right = a[i + offset + p]
a[i + offset] = left + right
a[i + offset + p] = (a[0].mod() +
left.val() - right.val()) * inow.val()
inow *= sum_ie[atcoder._bit._bsf(~s)]
def convolution_mod(a: typing.List[Modint],
b: typing.List[Modint]) -> typing.List[Modint]:
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 60:
if n < m:
n, m = m, n
a, b = b, a
ans = [Modint(0) for _ in range(n + m - 1)]
for i in range(n):
for j in range(m):
ans[i + j] += a[i] * b[j]
return ans
z = 1 << atcoder._bit._ceil_pow2(n + m - 1)
while len(a) < z:
a.append(Modint(0))
_butterfly(a)
while len(b) < z:
b.append(Modint(0))
_butterfly(b)
for i in range(z):
a[i] *= b[i]
_butterfly_inv(a)
a = a[:n + m - 1]
iz = Modint(z).inv()
for i in range(n + m - 1):
a[i] *= iz
return a
def convolution(mod: int, a: typing.List[typing.Any],
b: typing.List[typing.Any]) -> typing.List[typing.Any]:
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
with ModContext(mod):
a2 = list(map(Modint, a))
b2 = list(map(Modint, b))
return list(map(lambda c: c.val(), convolution_mod(a2, b2)))
def convolution_int(
a: typing.List[int], b: typing.List[int]) -> typing.List[int]:
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
mod1 = 754974721 # 2^24
mod2 = 167772161 # 2^25
mod3 = 469762049 # 2^26
m2m3 = mod2 * mod3
m1m3 = mod1 * mod3
m1m2 = mod1 * mod2
m1m2m3 = mod1 * mod2 * mod3
i1 = atcoder._math._inv_gcd(mod2 * mod3, mod1)[1]
i2 = atcoder._math._inv_gcd(mod1 * mod3, mod2)[1]
i3 = atcoder._math._inv_gcd(mod1 * mod2, mod3)[1]
c1 = convolution(mod1, a, b)
c2 = convolution(mod2, a, b)
c3 = convolution(mod3, a, b)
c = [0] * (n + m - 1)
for i in range(n + m - 1):
c[i] += (c1[i] * i1) % mod1 * m2m3
c[i] += (c2[i] * i2) % mod2 * m1m3
c[i] += (c3[i] * i3) % mod3 * m1m2
c[i] %= m1m2m3
return c
"""
atcoder.convolution = types.ModuleType('atcoder.convolution')
atcoder.convolution.__dict__['atcoder'] = atcoder
atcoder.convolution.__dict__['atcoder._bit'] = atcoder._bit
atcoder.convolution.__dict__['atcoder._math'] = atcoder._math
atcoder.convolution.__dict__['ModContext'] = atcoder.modint.ModContext
atcoder.convolution.__dict__['Modint'] = atcoder.modint.Modint
exec(_atcoder_convolution_code, atcoder.convolution.__dict__)
convolution_int = atcoder.convolution.convolution_int
# https://atcoder.jp/contests/practice2/tasks/practice2_f
import sys
# from atcoder.convolution import convolution_int
def main() -> None:
n, m = map(int, sys.stdin.readline().split())
a = list(map(int, sys.stdin.readline().split()))
b = list(map(int, sys.stdin.readline().split()))
c = convolution_int(a, b)
print(' '.join([str(ci % 998244353) for ci in c]))
if __name__ == '__main__':
main()
```
No
| 97,604 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
'''
参考:
https://maspypy.com/%E6%95%B0%E5%AD%A6%E3%83%BBnumpy-%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9Bfft%E3%81%AB%E3%82%88%E3%82%8B%E7%95%B3%E3%81%BF%E8%BE%BC%E3%81%BF
'''
import numpy as np
from numpy.fft import rfft,irfft
def convolve(a1,a2):
n = 2**(len(a1)+len(a2)+1).bit_length()
b1,b2=np.zeros(n),np.zeros(n)
b1[:len(a1)], b2[:len(a2)]= a1,a2
return (irfft(rfft(b1)*rfft(b2))+0.5).astype(int)
def convolve_large(f,g,mod,shift=15):
f1,f2 = np.divmod(f,1<<shift)
g1,g2 = np.divmod(g,1<<shift)
a = convolve(f1,g1) % mod
c = convolve(f2,g2) % mod
b = (convolve(f1+f2,g1+g2) - (a+c)) % mod
h = (a << shift*2) + (b << shift) + c
return h % mod
def convolve_large2(f,g,mod,shift=15):
f1,f2 = np.divmod(f,1<<shift)
g1,g2 = np.divmod(g,1<<shift)
a = convolve_large(f1,g1,mod) % mod
c = convolve_large(f2,g2,mod) % mod
b = (convolve_large(f1+f2,g1+g2,mod) - (a+c)) % mod
h = (a << shift*2) + (b << shift) + c
return h % mod
N,M=map(int,input().split())
*A,=map(int,input().split())
*B,=map(int,input().split())
mod = 998244353
print(*convolve_large2(A,B,mod,30)[:N+M-1])
```
No
| 97,605 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.
Constraints
* 1 \leq N, M \leq 524288
* 0 \leq a_i, b_i < 998244353
* All values in Input are integer.
Input
Input is given from Standard Input in the following format:
N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Output
Print the answer in the following format:
c_0 c_1 ... c_{(N - 1) + (M - 1)}
Examples
Input
4 5
1 2 3 4
5 6 7 8 9
Output
5 16 34 60 70 70 59 36
Input
1 1
10000000
10000000
Output
871938225
Submitted Solution:
```
k, K = 80, 1 << 80
nu = lambda L: int("".join([bin(a)[2:].zfill(k) for a in L[::-1]]), 2)
st = lambda n: bin(n)[2:].zfill((len(A)+len(B)-1)*k) + "_"
li = lambda s: [int(a, 2) % 998244353 for a in [s[-(i+1)*k-1:-i*k-1] for i in range(len(A)+len(B)-1)]]
input()
A = [int(a) for a in input().split()]
B = [int(a) for a in input().split()]
print(*li(st(nu(A) * nu(B))))
```
No
| 97,606 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
X=int(input())
c=int(100)
i=0
while c<X:
c=int(1.01*c)
i+=1
print(i)
```
| 97,607 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
x=int(input())
a=100
b=0
while a<x:
a=int(a*1.01)
b+=1
print(b)
```
| 97,608 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
X=int(input())
t=100
ans=0
while t<X:
ans+=1
t=int(t*1.01)
print(ans)
```
| 97,609 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
#abc165b
x=float(input())
p=100.0
s=0
while p<x:
p+=p//100
s+=1
print(s)
```
| 97,610 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
x=int(input())
n=100
k=0
while n<x:
n=n*101//100
k+=1
print(k)
```
| 97,611 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
x=int(input())
y=0
mon=100
while x>mon:
mon+=mon//100
y+=1
print(y)
```
| 97,612 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
X=int(input())
c=100
d=0
while c<X:
c=int(c*1.01)
d+=1
print(d)
```
| 97,613 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
"Correct Solution:
```
X=int(input())
p=100;ytd=0
while p<X:
p=int(p*1.01)
ytd=ytd+1
print(ytd)
```
| 97,614 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
x=int(input())
n=100
ans=0
while n<x:
ans+=1
n+=int(n/100)
print(ans)
```
Yes
| 97,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
x=int(input())
i=0
s=100
while s<x:
s=int(s*1.01)
i+=1
print(i)
```
Yes
| 97,616 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
x=int(input())
m=100
y=0
while m<x:
y+=1
m=int(m*1.01)
print(y)
```
Yes
| 97,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
X=int(input())
y=100
i=0
while y<X:
y=int(y*1.01)
i+=1
print(i)
```
Yes
| 97,618 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
x=int(input())
a=100
k=0
while(1):
k+=1
a=a+a(1//100)
if(a>=x):break
print(k)
```
No
| 97,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
def compound_interest(principle, rate, time):
CI = principle * (pow((1 + rate / 100), time))
return CI
x=int(input())
for i in range (1,100000):
ci=int(compound_interest(100, 1, i))
if(ci>=x):
print(i)
break
```
No
| 97,620 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
x = int(input())
i = 0
k = 100
while True:
if(k>=x):
break
else:
k*=1.01
i+=1
print(i)
```
No
| 97,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.
The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)
Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?
Constraints
* 101 \le X \le 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X
Output
Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.
Examples
Input
103
Output
3
Input
1000000000000000000
Output
3760
Input
1333333333
Output
1706
Submitted Solution:
```
X = input()
Money = 100
counter = 0
while int(X) > Money:
Money = Money*1.01
counter = counter + 1
print(counter)
```
No
| 97,622 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n,a,b=map(int,input().split())
if (b-a-1)%2==1:
print((b-a-1)//2+1)
else:
print(min(a-1,n-b)+1+(b-a-2)//2+1)
```
| 97,623 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n,a,b=map(int,input().split())
if (b-a)%2==0:
print((b-a)//2)
else:
print(min(a-1+1+(b-a-1)//2,n-b+1+(n-(a+n-b+1))//2))
```
| 97,624 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n,a,b = map(int,input().split())
if (b-a)%2==0:
print(int((b-a)//2))
else:
print(int(min(a-1,n-b)+1+(b-1-a)//2))
```
| 97,625 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n, a, b = map(int, input().split())
dif = b-a
if dif%2 == 0:
print(dif//2)
else:
print(min(a-1, n-b)+1+(b-a-1)//2)
```
| 97,626 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n, a, b = map(int, input().split())
d = b - a
print((d % 2 and min(a, n - b + 1)) + d // 2)
```
| 97,627 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n,a,b=map(int,input().split())
print((b-a)//2 if (b-a)%2==0 else min(a-1,n-b)+(b-a)//2+1)
```
| 97,628 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
n,a,b=map(int,input().split())
if (b-a)%2==0:
print((b-a)//2)
else:
c=b-a+1
print(c%2+c//2+min(a-1,n-b))
```
| 97,629 |
Provide a correct Python 3 solution for this coding contest problem.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
"Correct Solution:
```
N, A, B = map(int, input().split())
dif = B-A
if dif%2 == 0:
print(dif//2)
else:
print(min(A-1, N-B)+1+dif//2)
```
| 97,630 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
n,a,b=map(int,input().split())
if (b-a)%2==0:
print((b-a)//2)
else:
x=min(a-1,n-b)
y=(b-a-1)//2
print(x+y+1)
```
Yes
| 97,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
N,A,B = map(int,input().split())
if((B-A+1)%2==1):
print((B-A)//2)
else:
print(min(A-1,N-B)+1+(B-A-1)//2)
```
Yes
| 97,632 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
N, A, B = map(int,input().split())
if (A-B)%2 == 0:
print(abs(A-B)//2)
else:
print(min((A+B-1)//2,(2*N-(A+B)+1)//2))
```
Yes
| 97,633 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
n,a,b= map(int, input().split())
if (b-a)%2==0:
print((b-a)//2)
else:
print(min((a-1)+((1+b-a)//2),(n-b)+(1+b-a)//2))
```
Yes
| 97,634 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
import math
n,a,b = map(int,input().split())
ans = ((b-a)/2)
if int(ans) == ans:
print(round(ans))
else:
print(math.ceil(ans))
```
No
| 97,635 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
n,a,b=map(int,input().split())
cnt=0
if (b-a)%2 == 0:
cnt=round(b-(b+a)/2)
print(cnt)
exit()
if (b-a)%2 == 1:
if a==1:
if b==n:
c=n-a
d=round(1+((b-1)-(((b-1)+a)/2)))
cnt=min(c,d)
print(cnt)
exit()
if b==n:
if a==1:
c=b-1
d=round(1+(b-(b+a+1)/2))
cnt=min(c,d)
print(cnt)
exit()
if a-1 >= n-b:
cnt=round(n-a)
print(cnt)
exit()
if a-1 <= n-b:
cnt=round(b-1)
print(cnt)
exit()
```
No
| 97,636 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
a = list(map(int, input().split()))
N,A,B = a[0],a[1],a[2]
dim = B - A
if dim % 2 == 0:
print(int(dim/2))
if dim % 2 == 1:
dimAN = N - A
dimBN = N - B
dimB1 = B - 1
dimA1 = A - 1
if dimAN > dimB1:#Aが1にいって折り返す
print(dimA1 + int((dim-1)/2)+1)
elif dimAN < dimB1:
print(dimBN + int((dim-1)/2)+1)
elif dimAN == dimB1:
print(dimB1 + int((dim-1)/2)+1)
```
No
| 97,637 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
2N players are running a competitive table tennis training on N tables numbered from 1 to N.
The training consists of rounds. In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses.
The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1.
Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N.
Two friends are playing their first round matches on distinct tables A and B. Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other?
Constraints
* 2 \leq N \leq 10^{18}
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the smallest number of rounds after which the friends can get to play a match against each other.
Examples
Input
5 2 4
Output
1
Input
5 2 3
Output
2
Submitted Solution:
```
n, a, b = map(int, input().split())
ab = b-a
if ab%2 == 0:
print(ab//2)
else:
if ab == 1:
print(b-1)
elif n-b > a:
if (b-(a-1)-1) %2==0:
print((b-a-1-1)//2 + (a-1))
else:
print((b-a-2-1)//2 + (a-1))
else:
if (n-(a+n-b))%2==0:
print((n-a+n-b)//2 + (n-b))
else:
print((n-a+n-b+1)//2 + (n-b))
```
No
| 97,638 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split())) + [0]
res, p = 0, 0
for i in range(N+1):
pp = B[i]+p
res += min(A[i], pp)
p = max(min(pp-A[i], B[i]), 0)
print(res)
```
| 97,639 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
N = int(input())
A = [int(i) for i in input().split()]
B = [int(i) for i in input().split()]
cnt = 0
for i in range(N):
cnt += min(A[i]+A[i+1], B[i])
if A[i] < B[i]:
A[i+1] = max(A[i+1]+A[i]-B[i], 0)
print(cnt)
```
| 97,640 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
ans=0
for i in range(N):
a=min(A[i],B[i])
B[i]-=a
b=min(A[i+1],B[i])
A[i+1]-=b
ans+=a+b
print(ans)
```
| 97,641 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ans = 0
for i in range(N):
a = min(A[i], B[i])
b = min(A[i+1], B[i] - a)
A[i+1] -= b
ans += (a + b)
print(ans)
```
| 97,642 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
f = lambda : list(map(int, input().split()))
n = int(input())
la = f()
lb = f()
tmp = 0
ans = 0
for i in range(n):
m = min(la[i], tmp+lb[i])
tmp = min(tmp+lb[i]-m, lb[i])
ans += m
print(ans + min(la[n], tmp))
```
| 97,643 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
N=int(input())
f=lambda:map(int,input().split())
*A,=f()
*B,=f()
cnt=0
for i in range(len(B)):
a=min(A[i], B[i])
cnt+=a
a=min(A[i+1],B[i]-a)
cnt+=a
A[i+1]-=a
print(cnt)
```
| 97,644 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
#!/usr/bin/env python3
n, p, *a = map(int, open(0).read().split())
c = 0
for a, b in zip(a, a[n:]):
c += min(p+a, b)
p = a - max(min(b-p, a), 0)
print(c)
```
| 97,645 |
Provide a correct Python 3 solution for this coding contest problem.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ans=0
for i in range(n):
ans+=min(b[i],a[i]+a[i+1])
n1=min(a[i],b[i])
b[i]-=n1
a[i+1]=max(0,a[i+1]-b[i])
print(ans)
```
| 97,646 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
n = int(input())
*a, = map(int, input().split())
*b, = map(int, input().split())
s = sum(a)
for i in range(n):
c = min(a[i], b[i])
a[i] -= c
b[i] -= c
a[i+1] = max(0, a[i+1]-b[i])
print(s - sum(a))
```
Yes
| 97,647 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
cnt=0
for i in range(n):
f_1 = min(a[i],b[i])
f_2 = max(0,min(a[i+1],b[i]-a[i]))
cnt += f_1+f_2
a[i] -= f_1
a[i+1] -= f_2
print(cnt)
```
Yes
| 97,648 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ans=0
for i in range(n):
ans+=min(a[i],b[i])
if b[i]-a[i]>0:
ans+=min(b[i]-a[i],a[i+1])
a[i+1]-=min(b[i]-a[i],a[i+1])
print(ans)
```
Yes
| 97,649 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
res = 0
for n in range(N):
b = min(A[n], B[n])
B[n] -= b
b2 = min(A[n + 1], B[n])
A[n + 1] -= b2
res += b + b2
print(res)
```
Yes
| 97,650 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
N = int(input())
A = [int(i) for i in input().split()]
B = [int(i) for i in input().split()]
ans = 0
bef = 0
for i in range(N):
A[i] -= bef
ans += bef
if B[i] < A[i]:
ans += B[i]
bef = 0
else:
ans += A[i]
bef = B[i] -A[i]
ans += min(A[-1],bef)
print(ans)
```
No
| 97,651 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
kill = 0
for i in range(n):
for j in range(i,i+2):
if b[i] <= a[j]:
kill += b[i]
a[j] -= b[i]
continue
else:
kill += a[j]
b[i] -= a[j]
print(kill)
```
No
| 97,652 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
ans=0
for i in range(N):
p=min(A[i]+A[i+1],B[i])
ans=ans+p
if A[i]+A[i+1]<=B[i]:
A[i+1]=max(0,A[i+1]-B[i])
print(ans)
```
No
| 97,653 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N+1 towns. The i-th town is being attacked by A_i monsters.
We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.
What is the maximum total number of monsters the heroes can cooperate to defeat?
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N
Output
Print the maximum total number of monsters the heroes can defeat.
Examples
Input
2
3 5 2
4 5
Output
9
Input
3
5 6 3 8
5 100 8
Output
22
Input
2
100 1 1
1 100
Output
3
Submitted Solution:
```
N = int(input())
A = input().split()
B = input().split()
for i in range(N+1):
A[i] = int(A[i])
for i in range(N):
B[i] = int(B[i])
Ans = 0
yo = 0
chinpo = True
for i in range(N-1):
if chinpo:
Ans += min(A[i],B[i])
if B[i] > A[i]:
yo = B[i] - A[i]
chinpo = False
else:
Ans += min(A[i],B[i]+yo)
chinpo = True
if yo >= A[i]:
yo = B[i]
chinpo = False
elif B[i]+yo >= A[i]:
yo = B[i]+B[i-1]-A[i-1]
chinpo = False
if not chinpo:
if B[N-1]+B[N-2]-A[N-2]-A[N-1] >= A[N]:
Ans += A[N]
else:
Ans += B[N-1]+B[N-2]-A[N-2]-A[N-1]
print(Ans)
```
No
| 97,654 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
n = int(input())
a = list(input())
b = list(set(a))
ans = 1
for i in b:
ans %= 10**9+7
ans *= a.count(i)+1
print((ans-1)%(10**9+7))
```
| 97,655 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
_,s=open(0);a=1
for i in set(s):a*=s.count(i)+1
print(a//2%(10**9+7)-1)
```
| 97,656 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
n=int(input())
s=input()
cnt=[0]*26
for i in s:cnt[ord(i)-ord('a')]+=1
mo=10**9+7
r=1
for i in cnt:
r*=i+1
r%=mo
print((r-1+mo)%mo)
```
| 97,657 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
N=int(input())
X=[0 for i in range(26)]
S=input()
for i in S:
X[ord(i)-97]+=1
ans=1
P=10**9+7
for i in X:
ans=ans*(i+1)
ans%=P
ans-=1
print(ans)
```
| 97,658 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
N = int(input())
S = input()
ans = 1
for c in range(ord('a'), ord('z') + 1):
ans *= S.count(chr(c)) + 1
print((ans-1) % (10**9 + 7))
```
| 97,659 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
from collections import Counter
n = int(input())
S = input()
mod = 10**9+7
n = Counter(S)
ans = 1
for i, j in n.items():
ans *= (j+1)
print((ans-1)%mod)
```
| 97,660 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
from collections import Counter
n=int(input())
s=input()
S=Counter(s)
ans=1
for i in S.values():
ans *=i+1
print((ans-1)%(10**9+7))
```
| 97,661 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
"Correct Solution:
```
MOD=10**9+7
N=int(input())
S=input()
cnt=[0]*26
for x in S:
cnt[ord(x)-97]+=1
res=1
for i in range(26):
res=res*(cnt[i]+1)%MOD
print(res-1)
```
| 97,662 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
n,s=open(0);a=1
for c in set(s.strip()):a*=s.count(c)+1
print(~-a%(10**9+7))
```
Yes
| 97,663 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
cnt = [0] * 26
n = int(input())
s = input()
for c in s:
cnt[ord(c) - ord('a')] += 1
res = 1
for i in cnt:
res *= i + 1
print((res - 1) % (10 ** 9 + 7))
```
Yes
| 97,664 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
n=int(input())
s=input()
mod=10**9+7
t=dict()
for c in s:
t.setdefault(c,1)
t[c]+=1
ans=1
for v in t.values():
ans=ans*v%mod
print(ans-1)
```
Yes
| 97,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
from collections import Counter
n,s=int(input()),input();c=[s[i]for i in range(n)];a=Counter(c);ans=1
for i in a:ans*=a[i]+1
print((ans-1)%(10**9+7))
```
Yes
| 97,666 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
import string
n = int(input())
s = input()
total = 2**n-1
k = 0
for i in string.ascii_lowercase:
c = s.count(i)
if c > 1:
l = 2**(n-c)
total -= l
k += c - 1
if k > 1:
total += k
print(total)
```
No
| 97,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
N = int(input())
S = input()
ans = 1
for c in [chr(x) for x in range(97, 97 + 26)]:
ans *= S.count(c) + 1
print(ans - 1)
```
No
| 97,668 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
N = int(input())
S = input()
iD = 10**9+7
aT={}
for s in S:
if s in aT:
aT[s]+=1
else:
aT[s]=1
iRes = (2**N) - 1
iC = 0
iC2 = 0
for s in aT:
iT = aT[s]
if 1 < iT:
iRes -= 2**(N-iT)
if 0 < iC :
iC2 += 2**(N-iC -iT)
iRes += iC2
iC += iT
print(iRes % iD)
```
No
| 97,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N. Among its subsequences, count the ones such that all characters are different, modulo 10^9+7. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.
Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.
Constraints
* 1 \leq N \leq 100000
* S consists of lowercase English letters.
* |S|=N
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of the subsequences such that all characters are different, modulo 10^9+7.
Examples
Input
4
abcd
Output
15
Input
3
baa
Output
5
Input
5
abcab
Output
17
Submitted Solution:
```
if __name__ == '__main__':
mod = 10**9 +7
N = int(input())
S = str(input())
letter = defaultdict(int)
for i in range(N):
letter[S[i]] += 1
count = 1
for c in letter:
count *= (letter[c]+1)
count%mod
print(count-1)
```
No
| 97,670 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
import math
N, M = [int(i) for i in input().split()]
for i in range(M//N, 0, -1):
if M % i == 0:
print(i)
break
```
| 97,671 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
N,M=map(int,input().split())
ans=0
for i in range(1,int(M**0.5)+1):
if M%i==0:
if M/i>=N: ans=max(ans,i)
if i>=N: ans=max(ans,M//i)
print(ans)
```
| 97,672 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
n, m = list(map(int, input().split(" ")))
ds = [x for x in range(1, int(m**.5)+1) if m%x==0]
ds = ds + [m//x for x in ds]
ds = [x for x in ds if x<=m//n]
print(max(ds))
```
| 97,673 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
N,M=map(int,input().split())
a=1
for i in range(1,4*10000):
if M%i:
continue
if M//i>=N and i>a:
a=i
if i>=N and M//i>a:
a=M//i
print(a)
```
| 97,674 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
from math import sqrt
N, M = map(int, input().split())
ans = max(M // i if M // i <= M / N else i for i in range(1, int(sqrt(M)) + 1) if M % i == 0 and i <= M / N)
print(ans)
```
| 97,675 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
n,m=map(int,input().split())
ans=1
for i in range(1,int(m**0.5)+1):
if m%i==0:
y=m//i
if m//i>=n and ans<i:
ans=i
if m//y>=n and ans<y:
ans=y
print(ans)
```
| 97,676 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
import sys
n,m=map(int,input().split())
a=m//n
ans=1
if m%n==0:
print(int(m//n))
sys.exit()
for i in range(1,a+1):
if m%i==0:
ans=max(ans,i)
print(ans)
```
| 97,677 |
Provide a correct Python 3 solution for this coding contest problem.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
"Correct Solution:
```
n,m = map(int,input().split())
ans = 1
for i in range(1,int(m**0.5)+1):
if m%i!=0:continue
if m//i>=n:
ans = max(i,ans)
if i>=n:
ans = max(m//i,ans)
print(ans)
```
| 97,678 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
n,m=map(int,input().split())
a=[]
for i in range(1,int(m**.5)+1):
if m%i==0:
if m//i>=n:a+=[i]
if i>=n:a+=[m//i]
print(max(a))
```
Yes
| 97,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
N,M=map(int,input().split())
base=M//N
li=[]
for i in range(1,int(pow(M,1/2))+1):
if i<=base and M%i==0:
li.append(i)
if M%i==0 and M//i<=base:
li.append(M//i)
print(max(li))
```
Yes
| 97,680 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
N, M = map(int, input().split())
ans = 1
for i in range(1, int(M**0.5)+1):
if M % i == 0 and M//N >= i:
ans = max(ans, i)
if M//N >= M//i:
ans = max(ans, M//i)
print(ans)
```
Yes
| 97,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
N,M = map(int,input().split())
gcd = M//N
while gcd*N!=M:
gcd = M//N
N = 1+(M-1)//gcd
print(gcd)
```
Yes
| 97,682 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
n,m=map(int,input().split())
num=m//n
ans=0
for i in range(int(m**0.5),1,-1):
Num=i
if m%i==0:
Num1=m//i if m//i<=num else 0
if Num>num:
Num=0
ans=max(ans,Num,Num1)
print(ans)
```
No
| 97,683 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
# D - Partition
# Mの約数で、しかもN倍してもMを超えないもののうち、最大のものを探す
N, M = map(int, input().split())
x = 1
while x * N <= M:
if M % x == 0:
ans = x
x += 1
print(ans)
```
No
| 97,684 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
import math
N, M = map(int,input().split())
j=1
for i in range(1, int(math.sqrt(M))+2):
if M%i==0:
if i <= M//N and j < i:
j=i
if M/i <= M//N and j < M/i:
j=M/i
print(j)
```
No
| 97,685 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integers N and M.
Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* N \leq M \leq 10^9
Input
Input is given from Standard Input in the following format:
N M
Output
Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.
Examples
Input
3 14
Output
2
Input
10 123
Output
3
Input
100000 1000000000
Output
10000
Submitted Solution:
```
import sys
## io ##
def IS(): return sys.stdin.readline().rstrip()
def II(): return int(IS())
def MII(): return list(map(int, IS().split()))
def MIIZ(): return list(map(lambda x: x-1, MII()))
## dp ##
def DD2(d1,d2,init=0): return [[init]*d2 for _ in range(d1)]
def DD3(d1,d2,d3,init=0): return [DD2(d2,d3,init) for _ in range(d1)]
## math ##
def divc(x,y) -> int: return -(-x//y)
def divf(x,y) -> int: return x//y
def gcd(x,y):
while y: x,y = y,x%y
return x
def lcm(x,y): return x*y//gcd(x,y)
def enumerate_divs(n):
"""Return a tuple list of divisor of n"""
return [(i,n//i) for i in range(1,int(n**0.5)+1) if n%i==0]
def get_primes(n=10**3):
"""Return a list of prime numbers n or less"""
is_prime = [True]*(n+1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n**0.5)+1):
if not is_prime[i]: continue
for j in range(i*2, n+1, i): is_prime[j] = False
return [i for i in range(n+1) if is_prime[i]]
def prime_factor(n):
"""Return a list of prime factorization numbers of n"""
res = []
for i in range(2,int(n**0.5)+1):
while n%i==0: res.append(i); n //= i
if n != 1: res.append(n)
return res
## const ##
MOD=10**9+7
## libs ##
import itertools as it
import functools as ft
from collections import deque, Counter
from heapq import heapify, heappop, heappush
from bisect import bisect_left
#======================================================#
def main():
n, m = MII()
divs = enumerate_divs(m)
ans = []
h = m/n
for i,j in divs:
if i <= h:
ans.append(i)
if j <= h:
ans.append(i)
print(max(ans))
if __name__ == '__main__':
main()
```
No
| 97,686 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
import sys
N = int(input())
if N == 3:
print('2 5 63')
sys.exit()
if N == 4:
print('2 5 20 63')
sys.exit()
if N == 5:
print('2 3 6 4 9')
sys.exit()
S = '2 3 6 4 9'
N -= 5
print(S, end='')
if N == 1:
print(' 12')
sys.exit()
for i in range(5001):
Tmp1 = 6 * i + 8
Tmp2 = 6 * i + 10
if Tmp2 > 30000:
break
print(' %d %d' %(Tmp1, Tmp2) , end='')
N -= 2
if N == 0:
print()
sys.exit()
elif N == 1:
print(' 12')
sys.exit()
for i in range(5001):
Tmp1 = 12 * i + 15
Tmp2 = 12 * i + 21
if Tmp2 > 30000:
break
print(' %d %d' %(Tmp1, Tmp2), end='')
N -= 2
if N == 0:
print()
sys.exit()
elif N == 1:
print(' 12')
sys.exit()
for i in range(N):
Tmp1 = 6 * (i + 2)
if Tmp1 > 30000:
break
print(' %d' %(Tmp1) , end='')
print()
```
| 97,687 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
n = int(input())
ANS = []
even = [2, 10, 3, 9, 4, 8, 6, 12]
odd = [12, 2, 10, 3, 9, 4, 8, 6]
if n == 3:
print(2, 5, 63)
else:
p = n // 8
r = n % 8
if r % 2 == 0:
tmp = even
else:
tmp = odd
ANS += [12 * i + x for x in tmp for i in range(p)]
ANS += [12 * p + x for x in tmp[:r]]
print(*ANS)
```
| 97,688 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
n=int(input())
if n==3:
print(2,5,63)
else:
if n%2==0:
ans=[3,9]
cnt=2
for i in range(30001):
if i%6==2:
if i+2<=30000:
ans.append(i)
ans.append(i+2)
cnt+=2
if cnt==n:
break
else:
continue
if cnt<n:
for i in range(12,30001):
if i%12==3:
if i+9<=30000:
ans.append(i)
ans.append(i+6)
cnt+=2
if cnt==n:
break
else:
continue
if cnt<n:
for i in range(1,30001):
if i%6==0:
ans.append(i)
cnt+=1
if cnt==n:
break
print(*ans)
else:
ans=[3,6,9]
cnt=3
for i in range(30001):
if i%6==2:
if i+2<=30000:
ans.append(i)
ans.append(i+2)
cnt+=2
if cnt==n:
break
else:
continue
if cnt<n:
for i in range(12,30001):
if i%12==3:
if i+9<=30000:
ans.append(i)
ans.append(i+6)
cnt+=2
if cnt==n:
break
else:
continue
if cnt<n:
for i in range(7,30001):
if i%6==0:
ans.append(i)
cnt+=1
if cnt==n:
break
print(*ans)
```
| 97,689 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
n=int(input())
ret=[2,3,4] if n>=6 else [2,5,63] if n==3 else [2,5,20,63] if n==4 else [2,5,20,30,63]
if n>=6:
def getnext(a):
if a%6==0:
return a+2
elif a%6==2:
return a+1
elif a%6==3:
return a+1
elif a%6==4:
return a+2
while len(ret)<n:
ret.append(getnext(ret[-1]))
if sum(ret)%6==5:
ret[-1]=getnext(ret[-1])
elif sum(ret)%6!=0:
ret.remove((sum(ret)%6)+6)
ret.append(getnext(ret[-1]))
while sum(ret)%6!=0:
ret[-1]=getnext(ret[-1])
print(" ".join(map(str,ret)))
```
| 97,690 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
N = int(input())
if N == 3:
ans = [2, 3, 25]
else:
# [合計が6の倍数]を常に満たすように追加する
if N % 2 == 0:
As = [2, 10, 3, 9, 4, 8, 6, 12]
else:
As = [6, 2, 10, 3, 9, 4, 8, 12]
ans = []
for i in range(N):
ans.append(As[i % 8] + 12 * (i // 8))
print(' '.join(map(str, ans)))
```
| 97,691 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
n=int(input())
if n==3:exit(print(2,5,63))
l=[6,2,10,3,9,4,8,12]if n%2else[2,10,3,9,4,8,6,12]
for i in range(n):print(i//8*12+l[i%8],end=" ")
```
| 97,692 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
n = int(input())
ANS = []
A = [2, 10, 3, 9, 4, 8, 6, 12]
if n == 3:
print(2, 5, 63)
else:
p = n // 8
r = n % 8
ANS += [12 * i + a for a in A for i in range(p)]
ANS += [12 * p + a for a in A[:r]]
if r % 2 == 1:
ANS.pop()
ANS.append(12 * p + 12)
print(*ANS)
```
| 97,693 |
Provide a correct Python 3 solution for this coding contest problem.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
"Correct Solution:
```
import sys
stdin = sys.stdin
def li(): return [int(x) for x in stdin.readline().split()]
def li_(): return [int(x)-1 for x in stdin.readline().split()]
def lf(): return [float(x) for x in stdin.readline().split()]
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(ns())
def nf(): return float(ns())
def solve(n:int) -> list:
x6o2 = [(6*i+2, 6*i+4) for i in range(5000)]
x6o3 = [(12*i+3, 12*i+9) for i in range(2500)]
o6 = [6*i+6 for i in range(5000)]
x6 = []
for i in range(2500):
x6.append(x6o3[i])
x6.append(x6o2[2*i])
x6.append(x6o2[2*i+1])
ans = []
if n == 3:
ans = [2, 5, 63]
elif n <= 15000:
idx = n//2
for i, (mn,mx) in enumerate(x6[:idx]):
ans.extend([mn,mx])
if n%2:
ans = ans + [6]
else:
for i, (mn,mx) in enumerate(x6):
ans.extend([mn,mx])
for o6i in o6[:n-15000]:
ans.append(o6i)
return ans
n = ni()
print(*solve(n))
```
| 97,694 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
Submitted Solution:
```
# -*- coding: utf-8 -*-
from sys import stdin
d_in = lambda: int(stdin.readline()) # N = d_in()
MAX = 30000
N = d_in()
base = [3, 25, 2, 35, 55]
cand = []
for i in range(4, MAX // 2, 2):
cand.append(i)
cand.append(MAX - i)
for i in range(9, MAX // 2, 6):
cand.append(i)
cand.append(MAX - i)
ans = []
if N < 5:
ans.extend(base[:3])
if N == 4:
ans.append(MAX)
elif N % 2 == 1:
ans.extend(base)
ans.extend(cand[:N-5])
else:
ans.extend(base)
ans.append(MAX)
ans.extend(cand[:N-6])
print(*ans)
```
Yes
| 97,695 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
Submitted Solution:
```
import sys
from math import gcd
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7
def debug(res):
tot = sum(res)
for num in res:
if gcd(tot - num, num) == 1:
return False
return True
def resolve():
n = int(input())
if n == 3:
res = [2, 5, 63]
elif n == 4:
res = [2, 5, 20, 63]
elif n == 5:
res = [2, 5, 20, 30, 63]
else:
nums = [num for num in range(2, 30001) if num % 2 == 0 or num % 3 == 0]
res = [nums[i] for i in range(n)]
total = sum(res)
if total % 6 == 2:
res.pop(res.index(8))
for i in range(n, len(nums)):
if nums[i] % 6 == 0:
res.append(nums[i])
break
elif total % 6 == 3:
res.pop(res.index(9))
for i in range(n, len(nums)):
if nums[i] % 6 == 0:
res.append(nums[i])
break
elif total % 6 == 5:
res.pop(res.index(9))
for i in range(n, len(nums)):
if nums[i] % 6 == 4:
res.append(nums[i])
break
print(*res)
# print(debug(res))
if __name__ == '__main__':
resolve()
```
Yes
| 97,696 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
Submitted Solution:
```
import sys
N=int(input())
if N==3:
print(2,5,63)
sys.exit()
if N==4:
print(2,5,20,63)
sys.exit()
S=[]
L=[0,2,3,4]
for i in range(1,30001):
j=i%6
if j in L:
S.append(i)
if len(S)==N-1:
break
s=sum(S)
def f(L):
return print(' '.join(map(str,L)))
if s%6==0:
f(S+[30000])
elif s%6==2:
f(S+[29998])
elif s%6==3:
f(S+[29997])
elif s%6==5:
f(S[1:]+[29997,30000])
#print(len(S),s%6)
```
Yes
| 97,697 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
Submitted Solution:
```
N = int(input())
if N == 3:
ret = [2, 5, 63]
else:
ret = []
if N <= 15000:
if N % 3 == 0:
b = 4
else:
b = 2
a = N - b
else:
a = 15000 - N%2
b = N - a
for i in range(1, a+1):
ret.append(2*i)
for i in range(b):
ret.append(3*(2 * i + 1))
assert len(ret) == N
print(' '.join([str(_) for _ in ret]))
```
Yes
| 97,698 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = \\{a_{1}, a_{2}, ..., a_{N}\\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.
Constraints
* 3 \leq N \leq 20000
Input
Input is given from Standard Input in the following format:
N
Output
Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :
* The elements must be distinct positive integers not exceeding 30000.
* The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
* S is a special set.
If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.
Examples
Input
3
Output
2 5 63
Input
4
Output
2 5 20 63
Submitted Solution:
```
import random
def main():
N = int(input().strip())
cand = []
for i in range(30000 // 6):
cand.append(6 * i + 2)
cand.append(6 * i + 3)
cand.append(6 * i + 4)
cand.append(6 * i + 6)
while True:
S = [random.choice(cand) for _ in range(N)]
if sum(S) % 6 == 0:
break
return ' '.join(map(str, S))
if __name__ == '__main__':
print(main())
```
No
| 97,699 |
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