message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0, 1, ... n-1$. Print all sets, each of which is a subset of $U$ and includes $T$ as a subset. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 18$
* $0 \leq k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
5: 0 2
7: 0 1 2
13: 0 2 3
15: 0 1 2 3 | instruction | 0 | 21,997 | 5 | 43,994 |
"Correct Solution:
```
n = int(input())
d = list(map(int,input().split()))
for b in range(2**n):
a = bin(b)[2:]
a = a[::-1]
ans = []
for i in range(len(a)):
if a[i] == "1":
ans.append(i)
ans.sort()
flag = True
for i in d[1:]:
if i not in ans:
flag = False
break
if flag:
print(str(b)+":",*ans)
``` | output | 1 | 21,997 | 5 | 43,995 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0, 1, ... n-1$. Print all sets, each of which is a subset of $U$ and includes $T$ as a subset. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 18$
* $0 \leq k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
5: 0 2
7: 0 1 2
13: 0 2 3
15: 0 1 2 3 | instruction | 0 | 21,998 | 5 | 43,996 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
write = sys.stdout.write
N = int(readline())
k, *B = map(int, readline().split())
M = sum(1 << b for b in B)
if M == 0:
write("0:\n")
for i in range(1, 1 << N):
if i & M == M:
write("%d: %s\n" % (i, " ".join(str(j) for j in range(N) if i & (1 << j))))
``` | output | 1 | 21,998 | 5 | 43,997 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0, 1, ... n-1$. Print all sets, each of which is a subset of $U$ and includes $T$ as a subset. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 18$
* $0 \leq k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
5: 0 2
7: 0 1 2
13: 0 2 3
15: 0 1 2 3
Submitted Solution:
```
n = int(input())
k, *b_arr = map(int, input().split())
masks = [1 << x for x in range(n)]
b_mask = 0
for b in b_arr:
b_mask += 1 << b
for i in range(1 << n):
if i & b_mask != b_mask:
continue
sub = [idx for idx, mask in enumerate(masks) if i & mask != 0b00]
print('{}: {}'.format(i, ' '.join(map(str, sub)))) if len(sub) != 0 else print(f'{i}:')
``` | instruction | 0 | 21,999 | 5 | 43,998 |
Yes | output | 1 | 21,999 | 5 | 43,999 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0, 1, ... n-1$. Print all sets, each of which is a subset of $U$ and includes $T$ as a subset. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 18$
* $0 \leq k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
5: 0 2
7: 0 1 2
13: 0 2 3
15: 0 1 2 3
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Bitset II - Enumeration of Subsets II
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_11_B&lang=jp
"""
n = int(input())
_, *B = map(int, input().split())
B = set(B)
for x in range(2**n):
if all([x&1<<s for s in B]):
if x == 0:
print('0:')
else:
bits = [i for i, b in enumerate(f'{x:b}'[::-1]) if b == '1']
print(f'{x}: {" ".join(map(str, bits))}')
``` | instruction | 0 | 22,000 | 5 | 44,000 |
Yes | output | 1 | 22,000 | 5 | 44,001 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0, 1, ... n-1$. Print all sets, each of which is a subset of $U$ and includes $T$ as a subset. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 18$
* $0 \leq k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
5: 0 2
7: 0 1 2
13: 0 2 3
15: 0 1 2 3
Submitted Solution:
```
n=int(input())
U=[n-1-i for i in range(n)]
ind='0'+str(n)+'b'
t=list(map(int,input().split()))
T=t[1:]
for i in range(2**n):
compare=[int(j) for j in format(i,ind)]
disp=[U[j] for j in range(n) if compare[j]==1]
disp.reverse()
if sorted(list(set(T)&set(disp)))==T:
print(i,end=":")
if len(disp)!=0:
print(" "+' '.join(map(str,disp)),end="")
print()
``` | instruction | 0 | 22,001 | 5 | 44,002 |
Yes | output | 1 | 22,001 | 5 | 44,003 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a set $T$, which is a subset of $U$. The set $U$ consists of $0, 1, ... n-1$. Print all sets, each of which is a subset of $U$ and includes $T$ as a subset. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.
Constraints
* $1 \leq n \leq 18$
* $0 \leq k \leq n$
* $0 \leq b_i < n$
Input
The input is given in the following format.
$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$
$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
$d$: $e_0$ $e_1$ ...
Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.
Example
Input
4
2 0 2
Output
5: 0 2
7: 0 1 2
13: 0 2 3
15: 0 1 2 3
Submitted Solution:
```
if __name__ == "__main__":
bit = int(input())
k, *E = map(lambda x: int(x), input().split())
m = sum(1 << e for e in E)
if (0 == m):
print(f"0:")
for d in range(1, 1 << bit):
if (d & m == m):
print(f"{d}: ", end="")
print(" ".join([str(elem) for elem in range(bit) if d & (1 << elem)]))
``` | instruction | 0 | 22,002 | 5 | 44,004 |
Yes | output | 1 | 22,002 | 5 | 44,005 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
a, b = map(int, input().split())
if a == b:
print(a, 0, ' ', b, 1,sep='')
elif a == b - 1:
print(a, 9, ' ', b, 0,sep='')
elif a == 9 and b == 1:
print(9, 10)
else:
print(-1)
``` | instruction | 0 | 22,118 | 5 | 44,236 |
Yes | output | 1 | 22,118 | 5 | 44,237 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
da, db = map(int, input().split())
if da+1 == db:
print(da, db)
elif da == db:
print(db*10+1, db*10+2)
elif da == 9 and db == 1:
print(9, 10)
else:
print(-1)
``` | instruction | 0 | 22,119 | 5 | 44,238 |
Yes | output | 1 | 22,119 | 5 | 44,239 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
values = input().split()
a, b = int(values[0]), int(values[1])
if (a == b):
print(a * 10, b * 10 + 1)
elif (a + 1 == b):
print(a * 10 + 9, b * 10)
elif (a == 9 and b == 1):
print(9, 10)
else:
print(-1)
``` | instruction | 0 | 22,120 | 5 | 44,240 |
Yes | output | 1 | 22,120 | 5 | 44,241 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
s=list(map(int, input().split()))
d1=s[0]
d2=s[1]
diff=(d1-d2)*(d1-d2)
if d2-d1>=2:
print(-1)
else:
if d1>d2:
if d1==9 and d2==1:
print(9, 10)
else:
print(-1)
elif d2-d1==1:
print(10*d1+9, 10*d2)
else:
print(10*d1, 10*d2+1)
``` | instruction | 0 | 22,121 | 5 | 44,242 |
Yes | output | 1 | 22,121 | 5 | 44,243 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
a,b=map(int,input().split())
if(abs(a-b)>1):
print(-1)
elif(abs(a-b)==1):
n1=a*10+9
n2=b*10
print(n1,n2)
else:
n1=a*10+1
n2=b*10+2
print(n1,n2)
``` | instruction | 0 | 22,122 | 5 | 44,244 |
No | output | 1 | 22,122 | 5 | 44,245 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
a,b=map(int,input().split())
if(a==9 and b==1):
print(9,10)
exit()
if(abs(a-b)>1):
print(-1)
exit()
if(abs(a-b)==0):
print(a,"00"," ",a,"01",sep="")
exit()
print(a,"99"," ",b,"00",sep="")
``` | instruction | 0 | 22,123 | 5 | 44,246 |
No | output | 1 | 22,123 | 5 | 44,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
a,b = map(int,input().split())
if b - a == 0:
print(0,1)
elif b-a == 1:
print(9,0)
else:
print(-1)
``` | instruction | 0 | 22,124 | 5 | 44,248 |
No | output | 1 | 22,124 | 5 | 44,249 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation a + 1 = b with positive integers a and b, but Kolya forgot the numbers a and b. He does, however, remember that the first (leftmost) digit of a was d_a, and the first (leftmost) digit of b was d_b.
Can you reconstruct any equation a + 1 = b that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.
Input
The only line contains two space-separated digits d_a and d_b (1 ≤ d_a, d_b ≤ 9).
Output
If there is no equation a + 1 = b with positive integers a and b such that the first digit of a is d_a, and the first digit of b is d_b, print a single number -1.
Otherwise, print any suitable a and b that both are positive and do not exceed 10^9. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding 10^9.
Examples
Input
1 2
Output
199 200
Input
4 4
Output
412 413
Input
5 7
Output
-1
Input
6 2
Output
-1
Submitted Solution:
```
a, b = [int(x) for x in input().split()]
if a > b or b - a > 1: print(-1)
else:
if a == b: print(a * 10, a * 10 + 1)
else: print(a, b)
``` | instruction | 0 | 22,125 | 5 | 44,250 |
No | output | 1 | 22,125 | 5 | 44,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two integers x and y are compatible, if the result of their bitwise "AND" equals zero, that is, a & b = 0. For example, numbers 90 (10110102) and 36 (1001002) are compatible, as 10110102 & 1001002 = 02, and numbers 3 (112) and 6 (1102) are not compatible, as 112 & 1102 = 102.
You are given an array of integers a1, a2, ..., an. Your task is to find the following for each array element: is this element compatible with some other element from the given array? If the answer to this question is positive, then you also should find any suitable element.
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the number of elements in the given array. The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 4·106) — the elements of the given array. The numbers in the array can coincide.
Output
Print n integers ansi. If ai isn't compatible with any other element of the given array a1, a2, ..., an, then ansi should be equal to -1. Otherwise ansi is any such number, that ai & ansi = 0, and also ansi occurs in the array a1, a2, ..., an.
Examples
Input
2
90 36
Output
36 90
Input
4
3 6 3 6
Output
-1 -1 -1 -1
Input
5
10 6 9 8 2
Output
-1 8 2 2 8
Submitted Solution:
```
maxbits = 22
maxmask = 1<<22
dp = [-1]*(maxmask)
n = int(input())
a = [int(x) for x in input().split()]
b = a[:]
P = [0]*n
for i in range(n):
P[i]=(~a[i])&(maxmask-1)
for exp in range(maxbits):
for i in range(maxmask):
if i&(1<<exp):
if dp[i]==-1:
dp[i]=dp[i-(1<<exp)]
for i in range(n):
maxx = maxmask-1
print(dp[maxx^a[i]],end=" ")
``` | instruction | 0 | 22,309 | 5 | 44,618 |
No | output | 1 | 22,309 | 5 | 44,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two integers x and y are compatible, if the result of their bitwise "AND" equals zero, that is, a & b = 0. For example, numbers 90 (10110102) and 36 (1001002) are compatible, as 10110102 & 1001002 = 02, and numbers 3 (112) and 6 (1102) are not compatible, as 112 & 1102 = 102.
You are given an array of integers a1, a2, ..., an. Your task is to find the following for each array element: is this element compatible with some other element from the given array? If the answer to this question is positive, then you also should find any suitable element.
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the number of elements in the given array. The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 4·106) — the elements of the given array. The numbers in the array can coincide.
Output
Print n integers ansi. If ai isn't compatible with any other element of the given array a1, a2, ..., an, then ansi should be equal to -1. Otherwise ansi is any such number, that ai & ansi = 0, and also ansi occurs in the array a1, a2, ..., an.
Examples
Input
2
90 36
Output
36 90
Input
4
3 6 3 6
Output
-1 -1 -1 -1
Input
5
10 6 9 8 2
Output
-1 8 2 2 8
Submitted Solution:
```
maxbits = 22
maxmask = 1<<maxbits
dp = [-1]*(maxmask)
n = int(input())
a = [int(x) for x in input().split()]
b = a[:]
P = [0]*n
# for i in range(n):
# a[i]=(~a[i])&(maxmask-1)
for exp in range(maxbits):
for i in range(maxmask):
if i&(1<<exp):
if dp[i]==-1:
dp[i]=dp[i-(1<<exp)]
for i in range(n):
maxx = maxmask-1
print(dp[maxx^a[i]],end=" ")
``` | instruction | 0 | 22,310 | 5 | 44,620 |
No | output | 1 | 22,310 | 5 | 44,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Two integers x and y are compatible, if the result of their bitwise "AND" equals zero, that is, a & b = 0. For example, numbers 90 (10110102) and 36 (1001002) are compatible, as 10110102 & 1001002 = 02, and numbers 3 (112) and 6 (1102) are not compatible, as 112 & 1102 = 102.
You are given an array of integers a1, a2, ..., an. Your task is to find the following for each array element: is this element compatible with some other element from the given array? If the answer to this question is positive, then you also should find any suitable element.
Input
The first line contains an integer n (1 ≤ n ≤ 106) — the number of elements in the given array. The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 4·106) — the elements of the given array. The numbers in the array can coincide.
Output
Print n integers ansi. If ai isn't compatible with any other element of the given array a1, a2, ..., an, then ansi should be equal to -1. Otherwise ansi is any such number, that ai & ansi = 0, and also ansi occurs in the array a1, a2, ..., an.
Examples
Input
2
90 36
Output
36 90
Input
4
3 6 3 6
Output
-1 -1 -1 -1
Input
5
10 6 9 8 2
Output
-1 8 2 2 8
Submitted Solution:
```
n = int(input().strip())
arr = list(map(int,input().strip().split()))
memo = {}
answer = []
for i, a in enumerate(arr):
if memo.get(a):
answer.append(memo[a])
else:
for j in arr[i:]:
if j & a == 0:
memo.setdefault(j, a)
memo.setdefault(a, j)
answer.append(j)
break
else:
memo[a] = -1
answer.append(-1)
print(' '.join([str(x) for x in answer]))
``` | instruction | 0 | 22,311 | 5 | 44,622 |
No | output | 1 | 22,311 | 5 | 44,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider equation:
x2 + s(x)·x - n = 0,
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
Input
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
Submitted Solution:
```
def f(x):
ans = 0
while x > 0:
ans += x % 10
x //= 10
return ans
def f1(b, c):
D = b ** 2 - 4 * c
ans1 = (-b + D ** 0.5) / 2
ans2 = (-b - D ** 0.5) / 2
return [ans1, ans2]
n = int(input())
ans = 10 ** 19
for i in range(1, 99):
k = f1(i, -n)
k1, k2 = k[0], k[1]
if k1 == int(k1) and f(k1) == i:
if int(k1) ** 2 + i * int(k1) - n == 0:
ans = min(ans, int(k1))
if ans == 10 ** 19:
print(-1)
else:
print(int(ans))
``` | instruction | 0 | 22,330 | 5 | 44,660 |
Yes | output | 1 | 22,330 | 5 | 44,661 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider equation:
x2 + s(x)·x - n = 0,
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
Input
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
Submitted Solution:
```
# from random import randint
# def simulation(n):
# array = [1 for i in range(n)]
# dataEntries = []
# halfPills = 0
# while(len(array) > 0):
# selection = randint(0,len(array) - 1)
# if (array[selection] == 1):
# array[selection] = 0
# halfPills += 1
# elif (array[selection] == 0):
# halfPills -= 1
# array.pop(selection)
# if (len(array) != 0):
# prob = float(halfPills)/len(array)
# print("half pills ratio:", prob)
# dataEntries.append(prob)
# print("The jar is empty. So ratio is 1.0 in the end")
# dataEntries.append(1.0)
# return dataEntries
# print("Simulation#1 of pills = 50")
# data = simulation(50)
# print("Simulation#2 of pills = 50")
# data2 = simulation(50)
import math
def sum(a):
summation = 0
a = int(a)
while (a > 0):
temp = a%10
a /= 10
a = int(a)
summation += temp
return summation
def stupid(b, n):
check = b*b - 4*1*n
if (check < 0):
# print("negative")
return False,-1
ans1 = (-1*b + math.sqrt(check))/(2*1)
# print("ans1", ans1)
# print("sum: ", sum(int(ans1)))
if (math.ceil(ans1) == math.floor(ans1) and int(ans1) > 0 and sum(int(ans1)) == b):
return True, int(ans1)
ans2 = (-1*b - math.sqrt(check))/(2*1)
# print("ans2", ans2)
if (math.ceil(ans2) == math.floor(ans2) and int(ans2) > 0 and sum(int(ans2)) == b):
return True, int(ans2)
return False,-1
n = int(input())
maxB = 10*9
found = False
for i in range(1,maxB+1):
check, ans = stupid(i,(-1*n))
# print("i: ", i, check, ans)
if (check):
if ((ans*ans + sum(ans)*ans - n) != 0):
continue
print(ans)
found = True
break
if (found == False):
print(-1)
``` | instruction | 0 | 22,332 | 5 | 44,664 |
Yes | output | 1 | 22,332 | 5 | 44,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider equation:
x2 + s(x)·x - n = 0,
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
Input
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
Submitted Solution:
```
def calc_exp(n):
return n * ( n + sum(map(int, str(n))) )
n = int(input())
l, r = 0, 1<<62
while (l <= r):
mid = l+r >> 1
if (calc_exp(mid) < n):
l = mid+1
else:
r = mid-1
res = l
for i in range(max(1, res-100), res+100):
if (calc_exp(i) == n):
print(i)
break
else:
print(-1)
``` | instruction | 0 | 22,333 | 5 | 44,666 |
Yes | output | 1 | 22,333 | 5 | 44,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider equation:
x2 + s(x)·x - n = 0,
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
Input
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
Submitted Solution:
```
n= int(input())
l= 0
r = n
mim= n + 10
while l <= r:
mid = (l + r) // 2
s= str(mid)
su = 0
for h in range(len(s)):
su += int(s[h])
if mid * (mid + su) == n:
mim = min(mim, mid)
l = mid + 1
elif mid * mid > n:
r= mid - 1
else:
l = mid + 1
if mim > n:
print(-1)
else:
print(mim)
``` | instruction | 0 | 22,334 | 5 | 44,668 |
No | output | 1 | 22,334 | 5 | 44,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider equation:
x2 + s(x)·x - n = 0,
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
Input
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
Submitted Solution:
```
def f(x):
ans = 0
while x > 0:
ans += x % 10
x //= 10
return ans
def f1(b, c):
D = b ** 2 - 4 * c
ans1 = (-b + D ** 0.5) / 2
ans2 = (-b - D ** 0.5) / 2
return [ans1, ans2]
n = int(input())
ans = 10 ** 18
if n == 2:
print(1)
else:
for i in range(2, int(n ** 0.5) + 1):
if n % i == 0:
x1 = f(i)
x2 = f(n // i)
print(x1, x2)
h, h1 = f1(x1, -n), f1(x2, -n)
k1, k2, k3, k4 = h[0], h[1], h1[0], h1[1]
if k1 == int(k1) and k1 > 0:
ans = min(ans, k1)
if k1 == int(k2) and k2 > 0:
ans = min(ans, k2)
if k1 == int(k3) and k3 > 0:
ans = min(ans, k3)
if k1 == int(k4) and k4 > 0:
ans = min(ans, k4)
if ans == 10 ** 18:
print(-1)
else:
print(int(ans))
``` | instruction | 0 | 22,335 | 5 | 44,670 |
No | output | 1 | 22,335 | 5 | 44,671 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider equation:
x2 + s(x)·x - n = 0,
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
Input
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
Examples
Input
2
Output
1
Input
110
Output
10
Input
4
Output
-1
Note
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
Submitted Solution:
```
n = int(input())
x = int(round(n**0.5-0.499999))
y = int(round(x*0.999))
while (x >= y):
list_1 = list(map(int, str(x)))
s = 0
for i in list_1:
s = s + i
if (x*x+s*x-n)==0:
print(x)
break
else: x = x-1
if (not (x*x+s*x-n)==0) : print('-1')
``` | instruction | 0 | 22,337 | 5 | 44,674 |
No | output | 1 | 22,337 | 5 | 44,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have been given n distinct integers a1, a2, ..., an. You can remove at most k of them. Find the minimum modular m (m > 0), so that for every pair of the remaining integers (ai, aj), the following unequality holds: <image>.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5000, 0 ≤ k ≤ 4), which we have mentioned above.
The second line contains n distinct integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Print a single positive integer — the minimum m.
Examples
Input
7 0
0 2 3 6 7 12 18
Output
13
Input
7 1
0 2 3 6 7 12 18
Output
7
Submitted Solution:
```
s=input().split()
n=int(s[0])
k=int(s[1])
s=input().split()
for i in range(n):
s[i]=int(s[i])
m=max(s)
for i in range(n,m):
L=[]
for j in range(i):
L.append(0)
for j in range(n):
L[s[j]%i]+=1
if(len(L)-L.count(1)-L.count(0)<=k):
print(i)
break
``` | instruction | 0 | 22,370 | 5 | 44,740 |
No | output | 1 | 22,370 | 5 | 44,741 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have been given n distinct integers a1, a2, ..., an. You can remove at most k of them. Find the minimum modular m (m > 0), so that for every pair of the remaining integers (ai, aj), the following unequality holds: <image>.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5000, 0 ≤ k ≤ 4), which we have mentioned above.
The second line contains n distinct integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Print a single positive integer — the minimum m.
Examples
Input
7 0
0 2 3 6 7 12 18
Output
13
Input
7 1
0 2 3 6 7 12 18
Output
7
Submitted Solution:
```
s=input().split()
n=int(s[0])
k=int(s[1])
s=input().split()
for i in range(n):
s[i]=int(s[i])
m=max(s)
for i in range(n,m+1):
L=[]
for j in range(i):
L.append(0)
for j in range(n):
L[s[j]%i]+=1
if(len(L)-L.count(1)-L.count(0)<=k):
print(i)
break
``` | instruction | 0 | 22,371 | 5 | 44,742 |
No | output | 1 | 22,371 | 5 | 44,743 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have been given n distinct integers a1, a2, ..., an. You can remove at most k of them. Find the minimum modular m (m > 0), so that for every pair of the remaining integers (ai, aj), the following unequality holds: <image>.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5000, 0 ≤ k ≤ 4), which we have mentioned above.
The second line contains n distinct integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Print a single positive integer — the minimum m.
Examples
Input
7 0
0 2 3 6 7 12 18
Output
13
Input
7 1
0 2 3 6 7 12 18
Output
7
Submitted Solution:
```
s=input().split()
n=int(s[0])
k=int(s[1])
s=input().split()
for i in range(n):
s[i]=int(s[i])
m=max(s)
for i in range(n,m+2):
L=[]
for j in range(i):
L.append(0)
for j in range(n):
L[s[j]%i]+=1
o=0
for d in range(i):
if(L[d]>1):
o+=L[d]-1
if(o<=k):
print(i)
break
``` | instruction | 0 | 22,372 | 5 | 44,744 |
No | output | 1 | 22,372 | 5 | 44,745 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have been given n distinct integers a1, a2, ..., an. You can remove at most k of them. Find the minimum modular m (m > 0), so that for every pair of the remaining integers (ai, aj), the following unequality holds: <image>.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5000, 0 ≤ k ≤ 4), which we have mentioned above.
The second line contains n distinct integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Print a single positive integer — the minimum m.
Examples
Input
7 0
0 2 3 6 7 12 18
Output
13
Input
7 1
0 2 3 6 7 12 18
Output
7
Submitted Solution:
```
s=input().split()
n=int(s[0])
k=int(s[1])
s=input().split()
for i in range(n):
s[i]=int(s[i])
m=max(s)
for i in range(n,m+2):
L=[]
for j in range(i):
L.append(0)
for j in range(n):
L[s[j]%i]+=1
if(len(L)-L.count(1)-L.count(0)<=k):
print(i)
break
``` | instruction | 0 | 22,373 | 5 | 44,746 |
No | output | 1 | 22,373 | 5 | 44,747 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
f = lambda q: 1 + int((1 + 8 * q) ** 0.5) >> 1
a, b, c, d = map(int, input().split())
x, y = f(a), f(d)
if x * x - x - 2 * a or y * y - y - 2 * d: t = 'Impossible'
elif a + b + c == 0: t = '1' * y
elif b + c + d == 0: t = '0' * x
elif b + c - x * y: t = 'Impossible'
elif c: t = '1' * (y - b // x - 1) + '0' * (b % x) + '1' + '0' * (x - b % x) + '1' * (b // x)
else: t = '0' * x + '1' * y
print(t)
``` | instruction | 0 | 22,516 | 5 | 45,032 |
Yes | output | 1 | 22,516 | 5 | 45,033 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
a00, a01, a10, a11 = list(map(int, input().split()))
if sum([a00, a01, a10, a11]) == 0:
print(0)
exit(0)
z, j = 0, 0
if a01 != 0 or a10 != 0:
z = j = 1
while z * (z - 1) // 2 < a00:
z += 1
while j * (j - 1) // 2 < a11:
j += 1
if any([z * (z - 1) // 2 != a00,
j * (j - 1) // 2 != a11,
z * j != a10 + a01]):
print('Impossible')
exit(0)
n = z + j
for i in range(n):
if z > 0 and a01 >= j:
print('0', end='')
a01 -= j
z -= 1
else:
print('1', end='')
j -= 1
``` | instruction | 0 | 22,519 | 5 | 45,038 |
Yes | output | 1 | 22,519 | 5 | 45,039 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
a = [int(i) for i in input().split()]
if len(set(a)) > 2:
print('Impossible')
else:
s = ''
for ai in a:
if ai == a[0]:
s += '0'
else:
s += '1'
print(s)
``` | instruction | 0 | 22,520 | 5 | 45,040 |
No | output | 1 | 22,520 | 5 | 45,041 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
a00, a01, a10, a11 = map(int, input().split())
numZeros = 0
numOnes = 0
ans = True
for n0 in range(1, 2*a00 + 1):
if n0 * (n0 - 1) == 2 * a00:
numZeros = n0
break
elif n0 * (n0 - 1) > 2 * a00:
ans = False
break;
for n1 in range(1, 2*a11 + 1):
if n1 * (n1 - 1) == 2 * a11:
numOnes = n1
break
elif n1 * (n1 - 1) > 2 * a11:
ans = False
break;
res = []
def generateResult(x,a01, a10, n0, n1):
while n0 > 0 or n1 > 0:
if a01 >= n1 and n1 > 0:
if n0 >= 1:
res.append(0)
a01 = a01 - n1
n0 = n0-1
else:
return
elif a10 >= n0 and n0 > 0:
if n1 >= 1:
res.append(1)
a10 = a10 - n0
n1 = n1-1
else:
return
elif n0 > 0 and n1 > 0:
return
elif 0 < n0 == a01 + a10 + n0 + n1:
for i in range(n0):
res.append(0)
n0 = 0
elif 0 < n1 == a01 + a10 + n0 + n1:
for i in range(n1):
res.append(1)
n1 = 0
else:
return
if a01 > 0 or a10 > 0:
numOnes = max(numOnes, 1)
if a00 == a01 == a10 == a11 == 0:
print(1)
elif a11 == 0 and a00 == 0 and a10 == 1 and a01 == 0:
print("10")
elif a11 == 0 and a00 == 0 and a01 == 1 and a10 == 0:
print("01")
elif ans:
generateResult(res, a01, a10, numZeros, numOnes)
if len(res) == numZeros + numOnes:
print("".join(map(str, res)))
else:
print("Impossible")
else:
print("Impossible")
``` | instruction | 0 | 22,521 | 5 | 45,042 |
No | output | 1 | 22,521 | 5 | 45,043 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
a00, a01, a10, a11 = map(int, input().split())
numZeros = 0
numOnes = 0
ans = True
for n0 in range(1, 2*a00 + 1):
if n0 * (n0 - 1) == 2 * a00:
numZeros = n0
break
elif n0 * (n0 - 1) > 2 * a00:
ans = False
break;
for n1 in range(1, 2*a11 + 1):
if n1 * (n1 - 1) == 2 * a11:
numOnes = n1
break
elif n1 * (n1 - 1) > 2 * a11:
ans = False
break;
res = []
def generateResult(x,a01, a10, n0, n1):
while n0 > 0 or n1 > 0:
if a01 >= n1 and n1 > 0:
res.append(0)
a01 = a01 - n1
n0 = n0-1
elif a10 >= n0 and n0 > 0:
res.append(1)
a10 = a10 - n0
n1 = n1-1
elif n0 > 0 and n1 > 0:
return
elif 0 < n0 == a01 + a10 + n0 + n1:
for i in range(n0):
res.append(0)
n0 = 0
elif 0 < n1 == a01 + a10 + n0 + n1:
for i in range(n1):
res.append(1)
n1 = 0
else:
return
if numOnes == 0 or numZeros == 0:
if a10 > 0 or a01 > 0:
ans = False
if a00 == a01 == a10 == a11 == 0:
print(1)
elif ans:
generateResult(res, a01, a10, numZeros, numOnes)
if len(res) == numZeros + numOnes:
print("".join(map(str, res)))
else:
print("Impossible")
else:
print("Impossible")
``` | instruction | 0 | 22,523 | 5 | 45,046 |
No | output | 1 | 22,523 | 5 | 45,047 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,602 | 5 | 45,204 |
"Correct Solution:
```
n, k = map(int, input().split())
A = [*map(int, input().split())]
for i in range(k, n): print('Yes' if A[i-k] < A[i] else 'No')
``` | output | 1 | 22,602 | 5 | 45,205 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,603 | 5 | 45,206 |
"Correct Solution:
```
n, k = map(int, input().split(' '))
a = [int(tmp) for tmp in input().split(' ')]
[print('Yes') if a < b else print('No') for a, b in zip(a[:n - k], a[k:])]
``` | output | 1 | 22,603 | 5 | 45,207 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,604 | 5 | 45,208 |
"Correct Solution:
```
#!/usr/bin/env python3
n, k = map(int, input().split())
a = list(map(int, input().split()))
for i in range(k, n):
print(["No", "Yes"][a[i - k] < a[i]])
``` | output | 1 | 22,604 | 5 | 45,209 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,605 | 5 | 45,210 |
"Correct Solution:
```
n, k, *A = map(int, open(0).read().split())
for i in range(k, n):
if A[i-k] < A[i]:
print('Yes')
else:
print('No')
``` | output | 1 | 22,605 | 5 | 45,211 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,606 | 5 | 45,212 |
"Correct Solution:
```
N, K = map(int,input().split())
AA = list(map(int,input().split()))
for i in range(K,N):
if AA[i-K]<AA[i]:
print('Yes')
else:
print('No')
``` | output | 1 | 22,606 | 5 | 45,213 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,607 | 5 | 45,214 |
"Correct Solution:
```
n,k = map(int,input().split())
ls = list(map(int,input().split()))
for i in range(n-k):
print("Yes" if ls[i] < ls[i+k] else "No")
``` | output | 1 | 22,607 | 5 | 45,215 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,608 | 5 | 45,216 |
"Correct Solution:
```
N, K=map(int,input().split())
A=list(map(int,input().split()))
for i in range(1,N-K+1):
if A[K+i-1]/A[i-1]>1:
print("Yes")
else:
print("No")
``` | output | 1 | 22,608 | 5 | 45,217 |
Provide a correct Python 3 solution for this coding contest problem.
M-kun is a student in Aoki High School, where a year is divided into N terms.
There is an exam at the end of each term. According to the scores in those exams, a student is given a grade for each term, as follows:
* For the first through (K-1)-th terms: not given.
* For each of the K-th through N-th terms: the multiplication of the scores in the last K exams, including the exam in the graded term.
M-kun scored A_i in the exam at the end of the i-th term.
For each i such that K+1 \leq i \leq N, determine whether his grade for the i-th term is strictly greater than the grade for the (i-1)-th term.
Constraints
* 2 \leq N \leq 200000
* 1 \leq K \leq N-1
* 1 \leq A_i \leq 10^{9}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 A_3 \ldots A_N
Output
Print the answer in N-K lines.
The i-th line should contain `Yes` if the grade for the (K+i)-th term is greater than the grade for the (K+i-1)-th term, and `No` otherwise.
Examples
Input
5 3
96 98 95 100 20
Output
Yes
No
Input
3 2
1001 869120 1001
Output
No
Input
15 7
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Output
Yes
Yes
No
Yes
Yes
No
Yes
Yes | instruction | 0 | 22,609 | 5 | 45,218 |
"Correct Solution:
```
N, K = map(int, input().split())
A = list(map(int, input().split()))
for i in range(0,N-K):
print("Yes" if A[K+i]>A[i] else "No")
``` | output | 1 | 22,609 | 5 | 45,219 |
Provide a correct Python 3 solution for this coding contest problem.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes | instruction | 0 | 22,634 | 5 | 45,268 |
"Correct Solution:
```
from operator import itemgetter
class UnionFind:
def __init__(self, n):
self.table = [-1] * n
def _root(self, x):
if self.table[x] < 0:
return x
else:
self.table[x] = self._root(self.table[x])
return self.table[x]
def find(self, x, y):
return self._root(x) == self._root(y)
def union(self, x, y):
r1 = self._root(x)
r2 = self._root(y)
if r1 == r2:
return
d1 = self.table[r1]
d2 = self.table[r2]
if d1 <= d2:
self.table[r2] = r1
if d1 == d2:
self.table[r1] -= 1
else:
self.table[r1] = r2
def solve(n, aaa, bbb):
aai = sorted(enumerate(aaa), key=itemgetter(1))
bbi = sorted(enumerate(bbb), key=itemgetter(1))
uft = UnionFind(n)
for (ai, a), (bi, b) in zip(aai, bbi):
if a > b:
return False
uft.union(ai, bi)
if sum(r < 0 for r in uft.table) > 1:
return True
return any(a <= b for (ai, a), (bi, b) in zip(aai[1:], bbi))
n = int(input())
aaa = list(map(int, input().split()))
bbb = list(map(int, input().split()))
print('Yes' if solve(n, aaa, bbb) else 'No')
``` | output | 1 | 22,634 | 5 | 45,269 |
Provide a correct Python 3 solution for this coding contest problem.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes | instruction | 0 | 22,635 | 5 | 45,270 |
"Correct Solution:
```
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
A=[(A[i],i) for i in range(N)]
B=[(B[i],i) for i in range(N)]
check=True
Ainc=True
Binc=True
ABinc=True
A.sort()
B.sort()
for i in range(N):
if A[i][0]>B[i][0]:
check=False
if i>0:
if A[i-1]==A[i]:
Ainc=False
if B[i-1]==B[i]:
Binc=False
if B[i-1]>=A[i]:
ABinc=False
if not check:
print("No")
else:
if (not Ainc) or (not Binc) or (not ABinc):
print("Yes")
else:
edge=[[] for i in range(N)]
for i in range(N):
edge[A[i][1]].append(B[i][1])
que=[0]
while True:
v=que[-1]
nv=edge[v][0]
if nv==0:
break
else:
que.append(nv)
if len(que)==N:
print("No")
else:
print("Yes")
``` | output | 1 | 22,635 | 5 | 45,271 |
Provide a correct Python 3 solution for this coding contest problem.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes | instruction | 0 | 22,636 | 5 | 45,272 |
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
def count_loop(start, idx_map):
count = 0
idx = start
while True:
idx = idx_map[idx]
count += 1
if idx == 0:
break
return count
A, B = zip(*sorted(zip(A, B), key=lambda x: x[1]))
idx_map = sorted(range(N), key=lambda i: A[i])
A = sorted(A)
check_1 = all(A[i] <= B[i] for i in range(N))
check_2 = any(A[i + 1] <= B[i] for i in range(N - 1))
check_3 = count_loop(0, idx_map) <= N - 2
if check_1 and (check_2 or check_3):
print("Yes")
else:
print("No")
``` | output | 1 | 22,636 | 5 | 45,273 |
Provide a correct Python 3 solution for this coding contest problem.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes | instruction | 0 | 22,640 | 5 | 45,280 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
xa = sorted([(a[i], i) for i in range(N)], key = lambda x: x[0])
xb = sorted([(b[i], i) for i in range(N)], key = lambda x: x[0])
for i in range(N):
if xa[i][0] > xb[i][0]:
print("No")
exit(0)
class UnionFind():
def __init__(self, n):
self.n = n
self.root = [-1] * (n + 1)
self.rnk = [0] * (n + 1)
def Find_Root(self, x):
if self.root[x] < 0:
return x
else:
self.root[x] = self.Find_Root(self.root[x])
return self.root[x]
def Unite(self, x, y):
x = self.Find_Root(x)
y = self.Find_Root(y)
if x == y:
return
elif self.rnk[x] > self.rnk[y]:
self.root[x] += self.root[y]
self.root[y] = x
else:
self.root[y] += self.root[x]
self.root[x] = y
if self.rnk[x] == self.rnk[y]:
self.rnk[y] += 1
def isSameGroup(self, x, y):
return self.Find_Root(x) == self.Find_Root(y)
def Count(self, x):
return -self.root[self.Find_Root(x)]
uf = UnionFind(N)
c = 0
#print(xa, xb)
f = 0
for i in range(N):
#print((xa[i][1], xb[i][1]))
if uf.isSameGroup(xa[i][1], xb[i][1]):
c += 1
uf.Unite(xa[i][1], xb[i][1])
if c >= 2:
print("Yes")
else:
for i in range(N - 1):
if xa[i + 1] <= xb[i]:
print("Yes")
exit(0)
print("No")
``` | output | 1 | 22,640 | 5 | 45,281 |
Provide a correct Python 3 solution for this coding contest problem.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes | instruction | 0 | 22,641 | 5 | 45,282 |
"Correct Solution:
```
N = int(input())
A = [int(a) for a in input().split()]
B = [int(a) for a in input().split()]
A = [(A[i]<<18) + i for i in range(N)]
B = [(B[i]<<18) + i + (1<<17) for i in range(N)]
AA = sorted(A)
BB = sorted(B)
IA = {}
IB = {}
for i in range(N):
IA[AA[i]] = i
IB[BB[i]] = i
for i in range(N):
if AA[i] > BB[i]:
print("No")
break
else:
for i in range(1, N):
if AA[i] <= BB[i-1]:
print("Yes")
break
else:
for i in range(N):
if IA[A[i]] == IB[B[i]]:
print("Yes")
break
else:
c = 1
i = 0
P = [-1] * N
for i in range(N):
P[IA[A[i]]] = IB[B[i]]
i = P[0]
while i != 0:
i = P[i]
c += 1
if c < N:
print("Yes")
else:
print("No")
``` | output | 1 | 22,641 | 5 | 45,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes
Submitted Solution:
```
N = int(input())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]
A_s, B_s = sorted(A), sorted(B)
if any(a > b for a, b in zip(A_s, B_s)):
print("No")
quit()
A_idx = [(a, i) for i, a in enumerate(A)]
A_idx.sort()
B = [B[idx] for _, idx in A_idx]
B_idx = [(b, i) for i, b in enumerate(B)]
B_idx.sort()
perm = [0] * N
for i, (_, idx) in enumerate(B_idx):
perm[idx] = i
cycle_len = 0
used = [False] * N
for i in range(N):
if used[i]:
continue
cnt = 0
now = i
while not used[now]:
used[now] = True
cnt += 1
now = perm[now]
cycle_len += cnt - 1
if cycle_len < N - 1:
print("Yes")
quit()
if all(B_idx[i][0] < A_idx[i+1][0] for i in range(N-1)):
print("No")
else:
print("Yes")
``` | instruction | 0 | 22,642 | 5 | 45,284 |
Yes | output | 1 | 22,642 | 5 | 45,285 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes
Submitted Solution:
```
# encoding:utf-8
import copy
import random
import bisect #bisect_left これで二部探索の大小検索が行える
import fractions #最小公倍数などはこっち
import math
import sys
import bisect
mod = 10**9+7
sys.setrecursionlimit(mod) # 再帰回数上限はでdefault1000
def LI(): return list(map(int, sys.stdin.readline().split()))
N = int(input())
A = LI()
B = LI()
A, B = zip(*sorted(zip(A, B), key=lambda x:x[1]))
A_c = copy.deepcopy(A)
A = sorted(A)
B = sorted(B)
for i in range(N):
if A[i] > B[i]:
print("No")
sys.exit(0)
for i in range(1,N):
if A[i] < B[i-1]:
print("Yes")
sys.exit(0)
# ans = "Yes"
# for i in range(N):
# if A[i] <= B[i]:
# pass
# else:
# ans = "No"
# break
si2i = sorted(range(len(A_c)), key=lambda x:A_c[x])
a = 0
count = 0
while True:
a = si2i[a]
if a == 0:
break
count += 1
if count <= N - 2:
print("Yes")
else:
print("No")
``` | instruction | 0 | 22,643 | 5 | 45,286 |
Yes | output | 1 | 22,643 | 5 | 45,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes
Submitted Solution:
```
import sys
def wantp(n):
nq = []
while n != p[n]:
nq.append(n)
n = p[n]
for i in nq:
p[i] = n
return n
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
A2 = []
B2 = []
for i in range(N):
A2.append([A[i],i])
B2.append([B[i],i])
A2.sort()
B2.sort()
p = [i for i in range(N)]
rank = [1] * N
for i in range(N):
if A2[i][0] > B2[i][0]:
print ("No")
sys.exit()
for i in range(N):
na = A2[i][1]
nb = B2[i][1]
ap = wantp(na)
bp = wantp(nb)
if ap != bp:
if rank[ap] > rank[bp]:
p[bp] = ap
elif rank[bp] > rank[ap]:
p[ap] = bp
else:
p[ap] = bp
rank[bp] += 1
nloop = 0
for i in range(N):
if p[i] == i:
nloop += 1
if nloop != 1:
print ("Yes")
sys.exit()
for i in range(N-1):
if B2[i][0] >= A2[i+1][0]:
print ("Yes")
sys.exit()
print ("No")
``` | instruction | 0 | 22,644 | 5 | 45,288 |
Yes | output | 1 | 22,644 | 5 | 45,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes
Submitted Solution:
```
def solve(n, a_list, b_list):
a_list_s = sorted(a_list)
b_list_s = sorted(b_list)
# check 1
for i in range(n):
if a_list_s[i] > b_list_s[i]:
return "No"
# check 2
for i in range(n - 1):
if a_list_s[i + 1] <= b_list_s[i]:
return "Yes"
# check 3
# do it
# arg sort
a_list_s_arg = dict()
b_list_s_org = dict()
res_list = [0] * n
for j in range(n):
a_list_s_arg[a_list_s[j]] = j
for k in range(n):
b_list_s_org[b_list[k]] = k
for i in range(n):
j = a_list_s_arg[a_list[i]]
k = b_list_s_org[b_list_s[j]]
res_list[i] = k
i = 0
cnt = 0
while True:
i = res_list[i]
cnt += 1
if i == 0:
break
if cnt == n:
return "No"
else:
return "Yes"
def main():
n = int(input())
a_list = list(map(int, input().split()))
b_list = list(map(int, input().split()))
res = solve(n, a_list, b_list)
print(res)
def test():
assert solve(3, [1, 3, 2], [1, 2, 3]) == "Yes"
assert solve(3, [1, 2, 3], [2, 2, 2]) == "No"
assert solve(6, [3, 1, 2, 6, 3, 4], [2, 2, 8, 3, 4, 3]) == "Yes"
if __name__ == "__main__":
test()
main()
``` | instruction | 0 | 22,645 | 5 | 45,290 |
Yes | output | 1 | 22,645 | 5 | 45,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N. Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:
* Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
If the objective is achievable, print `Yes`; if it is not, print `No`.
Examples
Input
3
1 3 2
1 2 3
Output
Yes
Input
3
1 2 3
2 2 2
Output
No
Input
6
3 1 2 6 3 4
2 2 8 3 4 3
Output
Yes
Submitted Solution:
```
#!/usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
import sys, random, itertools, math
sys.setrecursionlimit(10**5)
input = sys.stdin.readline
sqrt = math.sqrt
def LI(): return list(map(int, input().split()))
def LF(): return list(map(float, input().split()))
def LI_(): return list(map(lambda x: int(x)-1, input().split()))
def II(): return int(input())
def IF(): return float(input())
def LS(): return list(map(list, input().split()))
def S(): return list(input().rstrip())
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 998244353
inf = float('INF')
#A
def A():
n = II()
n -= 1
print(n // 2)
return
#B
def combination_mod(n, k, mod=mod):
""" power_funcを用いて(nCk) mod p を求める """
""" nCk = n!/((n-k)!k!)を使用 """
from math import factorial
if n < 0 or k < 0 or n < k: return 0
if n == 0 or k == 0: return 1
a = factorial(n) % mod
b = factorial(k) % mod
c = factorial(n - k) % mod
return (a * pow(b, mod - 2, mod) * pow(c, mod - 2, mod)) % mod
def B():
n = II()
d = LI()
dic = defaultdict(int)
if d[0] != 0:
print(0)
return
for di in d[1:]:
dic[di] += 1
ans = 1
di = list(dic.items())
di.sort()
if di[0][0] != 1:
print(0)
return
for i in range(len(di) - 1):
if di[i][0] != di[i + 1][0] - 1:
print(0)
return
be = 1
for _, b in di:
ans *= pow(be, b, mod)
be = b
ans %= mod
print(ans)
return
class BinaryIndexedTree:
# http://hos.ac/slides/20140319_bit.pdf
def __init__(self, size):
"""
:param int size:
"""
self.bit = [0 for _ in range(size)]
self.size = size
def add(self, i, w):
"""
i番目にwを加える
:param int i:
:param int w:
:return:
"""
x = i + 1
while x <= self.size:
self.bit[x - 1] += w
x += x & -x
return
def sum(self, i):
"""
[0,i]の合計
:param int i:
:return:
"""
res = 0
x = i + 1
while x > 0:
res += self.bit[x - 1]
x -= x & -x
return res
def search(self, x):
"""
二分探索。和がx以上となる最小のインデックス(>= 1)を返す
:param int x:
:return :
"""
i = 1
s = 0
step = 1 << (self.size.bit_length() - 1)
while step:
if i + step <= self.size and s + self.bit[i + step - 1] < x:
i += step
s += self.bit[i - 1]
step >>= 1
return i
def __len__(self):
return self.size
#C
def C():
n = II()
a = LI()
b = LI()
res = None
for i in range(n):
if a[i] <= b[i]:
res = True
if res == None:
print("No")
return
ca = a[::1]
cb = b[::1]
ca.sort()
cb.sort()
d = [0] * n
for i in range(n):
if ca[i] > cb[i]:
print("No")
return
if i == 0:
continue
d[i] = ca[i] <= cb[i - 1]
d = list(itertools.accumulate(d))
for i in range(n):
if a[i] <= b[i]:
first = bisect_left(ca, a[i])
end = bisect_right(cb, b[i]) - 1
f = d[end] - d[first]
if f == end - first:
print("")
return
print("No")
return
def Dijkstra(num, start, vedge):
dist = [float("inf") for i in range(num)]
dist[0] = 0
for i in range(num):
du = dist[i]
l = i
for k, j in vedge[i]:
if dist[j] <= du + k:
continue
for j in range(j, i - 1, -1):
if dist[j] > du + k:
dist[j] = du + k
continue
break
return dist
#D
def D():
n, m = LI()
dist = [[] for i in range(n)]
for _ in range(m):
l, r, c = LI_()
c += 1
dist[l].append([c, r])
for i in range(n):
dist[i].sort()
dist = Dijkstra(n, 0, dist)
print(dist[n - 1] if dist[n - 1] != inf else -1)
return
#E
def E():
return
#F
def F():
return
#G
def G():
return
#H
def H():
return
#Solve
if __name__ == '__main__':
C()
``` | instruction | 0 | 22,646 | 5 | 45,292 |
No | output | 1 | 22,646 | 5 | 45,293 |
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