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 |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Compute A \times B.
Constraints
* 1 \leq A \leq 100
* 1 \leq B \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B
Output
Print the value A \times B as an integer.
Examples
Input
2 5
Output
10
Input
100 100
Output
10000
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
import numpy as np
import sys
if 0 in A:
print(0)
sys.exit()
ans = np.prod(A)
if ans<= 10**18:
print(ans)
sus.exit()
if 10**18 < ans:
print(-1)
``` | instruction | 0 | 71,396 | 5 | 142,792 |
No | output | 1 | 71,396 | 5 | 142,793 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Compute A \times B.
Constraints
* 1 \leq A \leq 100
* 1 \leq B \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B
Output
Print the value A \times B as an integer.
Examples
Input
2 5
Output
10
Input
100 100
Output
10000
Submitted Solution:
```
a = A
b = B
print(a*b)
``` | instruction | 0 | 71,397 | 5 | 142,794 |
No | output | 1 | 71,397 | 5 | 142,795 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Compute A \times B.
Constraints
* 1 \leq A \leq 100
* 1 \leq B \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B
Output
Print the value A \times B as an integer.
Examples
Input
2 5
Output
10
Input
100 100
Output
10000
Submitted Solution:
```
a,b = map(int,input().split())
print(a,b)
``` | instruction | 0 | 71,398 | 5 | 142,796 |
No | output | 1 | 71,398 | 5 | 142,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi's house has only one socket.
Takahashi wants to extend it with some number of power strips, each with A sockets, into B or more empty sockets.
One power strip with A sockets can extend one empty socket into A empty sockets.
Find the minimum number of power strips required.
Constraints
* All values in input are integers.
* 2 \leq A \leq 20
* 1 \leq B \leq 20
Input
Input is given from Standard Input in the following format:
A B
Output
Print the minimum number of power strips required.
Examples
Input
4 10
Output
3
Input
8 9
Output
2
Input
8 8
Output
1
Submitted Solution:
```
a,b=map(int,input().split())
k=0
while (a-1)*k+1<b:
k+=1
print(k)
``` | instruction | 0 | 71,424 | 5 | 142,848 |
Yes | output | 1 | 71,424 | 5 | 142,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi's house has only one socket.
Takahashi wants to extend it with some number of power strips, each with A sockets, into B or more empty sockets.
One power strip with A sockets can extend one empty socket into A empty sockets.
Find the minimum number of power strips required.
Constraints
* All values in input are integers.
* 2 \leq A \leq 20
* 1 \leq B \leq 20
Input
Input is given from Standard Input in the following format:
A B
Output
Print the minimum number of power strips required.
Examples
Input
4 10
Output
3
Input
8 9
Output
2
Input
8 8
Output
1
Submitted Solution:
```
a,b = map(int,input().split())
print((b-2)//(a-1)+1)
``` | instruction | 0 | 71,426 | 5 | 142,852 |
Yes | output | 1 | 71,426 | 5 | 142,853 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,439 | 5 | 142,878 |
"Correct Solution:
```
from collections import Counter
N = int(input())
As = list(map(int, input().split()))
cnt = Counter(As)
As.sort(reverse=True)
Ps = [2]
for i in range(29):
Ps.append(Ps[-1] * 2)
ans = 0
for A in As:
if cnt[A] <= 0: continue
cnt[A] -= 1
while Ps[-1] > 2 * A:
Ps.pop()
if cnt[Ps[-1] - A] > 0:
ans += 1
cnt[Ps[-1] - A] -= 1
print(ans)
``` | output | 1 | 71,439 | 5 | 142,879 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,440 | 5 | 142,880 |
"Correct Solution:
```
from collections import defaultdict
N = int(input())
A = list(map(int, input().split()))
A.sort()
d = defaultdict(int)
for a in A:
d[a] += 1
ans = 0
for i in range(N-1, -1, -1):
a = A[i]
if d[a] == 0:
continue
s = 2**(len(bin(a))-2)
p = s-a
if (d[p] > 0 and p!=a) or d[p]>1:
ans += 1
d[p] -= 1
d[a] -= 1
print(ans)
``` | output | 1 | 71,440 | 5 | 142,881 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,441 | 5 | 142,882 |
"Correct Solution:
```
import math
N = int(input())
a = sorted(list(map(int,input().split())))
count = 0
b = {}
for i in range(len(a)):
if a[i] in b:
b[a[i]] += 1
else:
b[a[i]] = 1
for i in range(len(a) - 1, -1, -1):
if b[a[i]] == 0:
continue
temp = a[i]
b[a[i]] -= 1
s=2**math.floor(math.log2(temp))
st = 2*s - temp
if a ==[]:
break
if st in b and b[st] > 0:
b[2*s-temp] -= 1
count += 1
print(count)
``` | output | 1 | 71,441 | 5 | 142,883 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,442 | 5 | 142,884 |
"Correct Solution:
```
import math
import bisect
n=int(input())
a=list(map(int,input().split()))
a.sort()
x=a[0];ctn=1;l=[];l2=[]
for i in range(1,n):
if x==a[i]:
ctn+=1
else:
l.append([x,ctn])
l2.append(x)
x=a[i]
ctn=1
l.append([x,ctn])
l2.append(x)
b=[2**i for i in range(1,50)]
ct=0
for i in range(len(l2)-1,-1,-1):
x=math.floor(math.log2(l2[i]))
x=b[x]-l2[i]
y=bisect.bisect_left(l2,x)
if l2[y]==x:
if l2[y]!=l2[i]:
m=min(l[i][1],l[y][1])
else:
m=l[i][1]//2
l[i][1]-=m
l[y][1]-=m
ct+=m
print(ct)
``` | output | 1 | 71,442 | 5 | 142,885 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,443 | 5 | 142,886 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse=True)
d = dict()
ans = 0
for x in a:
if x not in d:
d[x] = 0
d[x] += 1
for x in a:
t = (1<<x.bit_length()) - x
f = (d.get(t,0) and d.get(x,0))
if t == x:
f = (d.get(t,0) >= 2)
if f:
d[x] -= 1
d[t] -= 1
ans += 1
print(ans)
``` | output | 1 | 71,443 | 5 | 142,887 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,444 | 5 | 142,888 |
"Correct Solution:
```
from collections import Counter
N,*A = map(int, open(0).read().split())
Cnt = Counter(A)
m = 2**31
ans = 0
for i in range(31):
for k in Cnt.keys():
if Cnt[k]==0:
continue
if k==m-k:
ans += Cnt[k]//2
Cnt[k] %= 2
else:
if Cnt[m-k]==0:
continue
if Cnt[k]<Cnt[m-k]:
ans += Cnt[k]
Cnt[m-k] -= Cnt[k]
Cnt[k] = 0
else:
ans += Cnt[m-k]
Cnt[k] -= Cnt[m-k]
Cnt[m-k] = 0
m >>= 1
print(ans)
``` | output | 1 | 71,444 | 5 | 142,889 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,445 | 5 | 142,890 |
"Correct Solution:
```
from collections import Counter
N, *A = map(int, open(0).read().split())
A.sort(reverse=True)
C = Counter(A)
ans = 0
for a in A:
if C[a] == 0:
continue
C[a] -= 1
partner = (1 << (a.bit_length())) - a
if C[partner] > 0:
ans += 1
C[partner] -= 1
print(ans)
``` | output | 1 | 71,445 | 5 | 142,891 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2 | instruction | 0 | 71,446 | 5 | 142,892 |
"Correct Solution:
```
n = int(input())
a = list(map(int,input().split()))
a.sort()
from collections import Counter
dic = Counter(a)
ans = 0
for k in range(len(a)-1,-1,-1):
if dic[a[k]]==0:
continue
dic[a[k]] -= 1
t = 2**a[k].bit_length()-a[k]
if dic[t]:
dic[t] -= 1
ans += 1
print(ans)
``` | output | 1 | 71,446 | 5 | 142,893 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
from collections import*
N,*A=map(int, open(0).read().split())
A.sort()
C=Counter(A)
s=0
for a in A[::-1]:
if not C[a]:
continue
C[a]-=1
b=2**a.bit_length()-a
if C[b]:
C[b]-=1
s += 1
print(s)
``` | instruction | 0 | 71,447 | 5 | 142,894 |
Yes | output | 1 | 71,447 | 5 | 142,895 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
from collections import*
n,*a=map(int,open(0).read().split())
C=Counter(a)
r=0
for x in sorted(a)[::-1]:
if C[x]>0:y=1<<x.bit_length();C[x]-=1;r+=C[y-x]>0;C[y-x]-=1
print(r)
``` | instruction | 0 | 71,448 | 5 | 142,896 |
Yes | output | 1 | 71,448 | 5 | 142,897 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
from math import log,floor
from collections import Counter
N = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
C = Counter(A)
cnt = 0
last_a = -1
for i in range(N):
a = A[i]
if last_a == a:
continue
last_a = a
count_a = C[a]
if count_a <= 0:
continue
b = pow(2,floor(log(a)/log(2))+1) - a
count_b = C[b]
if count_b <= 0:
continue
i += count_a - 1
x = min(count_a, count_b) if a != b else count_a // 2
cnt += x
C[a] -= x
C[b] -= x
print(cnt)
``` | instruction | 0 | 71,449 | 5 | 142,898 |
Yes | output | 1 | 71,449 | 5 | 142,899 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
from collections import Counter
N, *A = map(int, open(0).read().split())
A.sort(reverse=True)
C = Counter(A)
ans = 0
for a in A:
if C[a] == 0:
continue
C[a] -= 1
partner = (2 ** (a.bit_length())) - a
if C[partner] > 0:
ans += 1
C[partner] -= 1
print(ans)
``` | instruction | 0 | 71,450 | 5 | 142,900 |
Yes | output | 1 | 71,450 | 5 | 142,901 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
import math
import bisect
n=int(input())
a=list(map(int,input().split()))
a.sort()
b=[]
for i in range(1,50):
b.append(2**i)
ct=0
check=[1]*n
ctb=0
w=2
for i in range(n):
if a[i] in b:
if a[i]==w:
ctb+=1
check[i]=0
else:
ct+=ctb//2
w=a[i]
check[i]=0
ctb=1
else:
ct+=ctb//2
ctb=0
ct+=ctb//2
for i in range(n-1,-1,-1):
if a[i]==1:
break
if check[i]==1:
check[i]=0
x=math.floor(math.log2(a[i]))
x=b[x]-a[i]
y=bisect.bisect_left(a,x)
z=bisect.bisect_right(a,x)
t=bisect.bisect_left(check[y:z],1)+y
if t!=z:
check[t]=0
ct+=1
ct1=0
for j in range(i+1):
if check[j]==1:
ct1+=1
ct+=ct1//2
print(ct)
``` | instruction | 0 | 71,451 | 5 | 142,902 |
No | output | 1 | 71,451 | 5 | 142,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
A=sorted(A)
from collections import Counter as co
D=co(A)
cnt=0
for i in range(N):
if D[A[-1-i]]>0:
D[A[-1-i]]-=1
for j in range(1,16):
d=2**j
if A[-1-i]<d:
e=d-A[-1-i]
break
if D[e]>0:
cnt+=1
D[e]-=1
print(cnt)
``` | instruction | 0 | 71,452 | 5 | 142,904 |
No | output | 1 | 71,452 | 5 | 142,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
import bisect
import math
N = int(input())
A = list(map(int, input().split()))
A.sort()
already = set()
def is_in(t, n):
i = bisect.bisect_right(A, t) - 1
if i > n or i < 0:
return False
while t == A[i]:
if i not in already:
already.add(i)
return True
i -= 1
if i < 0:
return False
return False
res = 0
for n in range(len(A) - 1, -1, -1):
if n in already:
continue
a = A[n]
t = 1 << (int(math.log2(a)) + 1)
while t > a:
if is_in(t - a, n):
res += 1
break
t >>= 1
print(res)
``` | instruction | 0 | 71,453 | 5 | 142,906 |
No | output | 1 | 71,453 | 5 | 142,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Examples
Input
3
1 2 3
Output
1
Input
5
3 11 14 5 13
Output
2
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
group = {}
for i in range(n):
ntz = a[i] & (-a[i])
if ntz not in group:
group[ntz] = {}
group[ntz][a[i] // (ntz*2)] = 1
elif a[i] // (ntz*2) not in group[ntz]:
group[ntz][a[i] // (ntz*2)] = 1
else:
group[ntz][a[i] // (ntz*2)] += 1
ans = 0
for ntz in group:
li = sorted(group[ntz].keys(), reverse = True)
for num1 in li:
tmp = len(bin(num1)) - 2
num2 = num1 ^ (2**tmp - 1)
if num2 == num1:
tmp_ans = group[ntz][num1] // 2
ans += tmp_ans
group[ntz][num1] -= tmp_ans * 2
continue
if num2 in group[ntz]:
tmp_ans = min(group[ntz][num1], group[ntz][num2])
ans += tmp_ans
group[ntz][num1] -= tmp_ans
group[ntz][num2] -= tmp_ans
print(ans)
``` | instruction | 0 | 71,454 | 5 | 142,908 |
No | output | 1 | 71,454 | 5 | 142,909 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
1
Output
)( | instruction | 0 | 71,577 | 5 | 143,154 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
n = I()
a = [0]
for i in range(1, 50000):
a.append(a[-1] + i)
t = bisect.bisect_left(a, n)
r = [1] * t + [0] * t
for i in range(t):
ai = a[t-i]
ti = t + i
# print(n,ai,ti,''.join(map(lambda x: '()'[x], r)))
if n < ai:
ts = min(t, ai-n)
r[ti],r[ti-ts] = r[ti-ts],r[ti]
n -= t - ts
else:
break
return ''.join(map(lambda x: '()'[x], r))
print(main())
``` | output | 1 | 71,577 | 5 | 143,155 |
Provide a correct Python 3 solution for this coding contest problem.
For given n points in metric space, find the distance of the closest points.
Constraints
* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100
Input
n
x0 y0
x1 y1
:
xn-1 yn-1
The first integer n is the number of points.
In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.
Output
Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.
Examples
Input
2
0.0 0.0
1.0 0.0
Output
1.000000
Input
3
0.0 0.0
2.0 0.0
1.0 1.0
Output
1.41421356237 | instruction | 0 | 71,596 | 5 | 143,192 |
"Correct Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
input:
3
0.0 0.0
2.0 0.0
1.0 1.0
output:
1.41421356237
"""
import math
import sys
from operator import attrgetter
class ClosestPair(object):
def __init__(self, ):
"""
Init closest pairs points set.
"""
_input = sys.stdin.readlines()
p_num = int(_input[0])
points = map(lambda x: x.split(), _input[1:])
p_list = [complex(float(x), float(y)) for x, y in points]
p_list.sort(key=attrgetter('real'))
# assert len(p_list) == p_num
# print(p_list)
ans = self.closest_pair(array=p_list, array_length=p_num)
print(('{:.6f}'.format(ans)))
def closest_pair(self, array, array_length):
if array_length <= 1:
return float('inf')
mid = array_length // 2
mid_real = array[mid].real
d = min(self.closest_pair(array[:mid], mid).real,
self.closest_pair(array[mid:], array_length - mid).real)
return self.brute_force(array, mid_real, d)
@staticmethod
def brute_force(array, mid_real, d=float('inf')):
array.sort(key=attrgetter('imag'))
min_stack = list()
for ele in array:
size = len(min_stack)
if abs(ele.real - mid_real) >= d:
continue
for j in range(size):
dx = ele.real - min_stack[size - j - 1].real
dy = ele.imag - min_stack[size - j - 1].imag
if dy >= d:
break
d = min(d, math.sqrt(dx ** 2 + dy ** 2))
min_stack.append(ele)
return d
if __name__ == '__main__':
case = ClosestPair()
``` | output | 1 | 71,596 | 5 | 143,193 |
Provide a correct Python 3 solution for this coding contest problem.
For given n points in metric space, find the distance of the closest points.
Constraints
* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100
Input
n
x0 y0
x1 y1
:
xn-1 yn-1
The first integer n is the number of points.
In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.
Output
Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.
Examples
Input
2
0.0 0.0
1.0 0.0
Output
1.000000
Input
3
0.0 0.0
2.0 0.0
1.0 1.0
Output
1.41421356237 | instruction | 0 | 71,601 | 5 | 143,202 |
"Correct Solution:
```
from sys import stdin
from operator import attrgetter
readline = stdin.readline
def norm(a):
return a.real * a.real + a.imag * a.imag
def closest_pair(p):
if len(p) <= 1:
return float('inf')
m = len(p) // 2
d = min(closest_pair(p[:m]), closest_pair(p[m:]))
p = [pi for pi in p if p[m].imag - d < pi.imag < p[m].imag + d]
return brute_force(p, d)
def brute_force(p, d=float('inf')):
p.sort(key=attrgetter('real'))
for i in range(1, len(p)):
for j in reversed(range(i)):
tmp = p[i] - p[j]
if d < tmp.real:
break
tmp = abs(tmp)
if d > tmp:
d = tmp
return d
def main():
n = int(readline())
p = [map(float, readline().split()) for _ in range(n)]
p = [x + y * 1j for x, y in p]
p.sort(key=attrgetter('imag'))
print('{:.6f}'.format(closest_pair(p)))
main()
``` | output | 1 | 71,601 | 5 | 143,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given n points in metric space, find the distance of the closest points.
Constraints
* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100
Input
n
x0 y0
x1 y1
:
xn-1 yn-1
The first integer n is the number of points.
In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.
Output
Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.
Examples
Input
2
0.0 0.0
1.0 0.0
Output
1.000000
Input
3
0.0 0.0
2.0 0.0
1.0 1.0
Output
1.41421356237
Submitted Solution:
```
from operator import attrgetter
from itertools import combinations
keys = [attrgetter('real'), attrgetter('imag')]
def solve(points, axis):
l = len(points)
if l < 20:
return min(abs(p2 - p1) for p1, p2 in combinations(points, 2))
m = l // 2
pl, pr = points[:m], points[m:]
key, rkey = keys[axis], keys[not axis]
ans = min(solve(sorted(pl, key=rkey), not axis),
solve(sorted(pr, key=rkey), not axis))
pm = key(pr[0])
for p in reversed(pl):
if key(p) <= pm - ans:
break
for q in pr:
if key(q) >= pm + ans:
break
rp = rkey(p)
if rp - ans < rkey(q) < rp + ans:
ans = min(ans, abs(q - p))
return ans
n = int(input())
points = [complex(*map(float, input().split())) for _ in range(n)]
print(solve(sorted(points, key=keys[0]), 0))
``` | instruction | 0 | 71,608 | 5 | 143,216 |
No | output | 1 | 71,608 | 5 | 143,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given n points in metric space, find the distance of the closest points.
Constraints
* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100
Input
n
x0 y0
x1 y1
:
xn-1 yn-1
The first integer n is the number of points.
In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.
Output
Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.
Examples
Input
2
0.0 0.0
1.0 0.0
Output
1.000000
Input
3
0.0 0.0
2.0 0.0
1.0 1.0
Output
1.41421356237
Submitted Solution:
```
from operator import attrgetter
from itertools import combinations
keys = [attrgetter('real'), attrgetter('imag')]
def bound(points):
xmx = max(p.real for p in points)
xmn = min(p.real for p in points)
ymx = max(p.imag for p in points)
ymn = min(p.imag for p in points)
return xmx - xmn < ymx - ymn
def solve(points, prev_sort):
l = len(points)
if l < 20:
return min(abs(p2 - p1) for p1, p2 in combinations(points, 2))
m = l // 2
pl, pr = points[:m], points[m:]
key, rkey = keys[prev_sort], keys[not prev_sort]
pl_next_sort, pr_next_sort = bound(pl), bound(pr)
pl_next_points = pl.copy() if prev_sort == pl_next_sort else sorted(pl, key=keys[pl_next_sort])
pr_next_points = pr.copy() if prev_sort == pr_next_sort else sorted(pr, key=keys[pr_next_sort])
ans = min(solve(pl_next_points, pl_next_sort), solve(pr_next_points, pr_next_sort))
pm = key(pr[0])
for p in reversed(pl):
if key(p) <= pm - ans:
break
for q in pr:
if key(q) >= pm + ans:
break
rp = rkey(p)
if rp - ans < rkey(q) < rp + ans:
ans = min(ans, abs(q - p))
return ans
n = int(input())
points = [complex(*map(float, input().split())) for _ in range(n)]
print('{:.10f}'.format(solve(sorted(points, key=keys[0]), 0)))
``` | instruction | 0 | 71,609 | 5 | 143,218 |
No | output | 1 | 71,609 | 5 | 143,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given n points in metric space, find the distance of the closest points.
Constraints
* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100
Input
n
x0 y0
x1 y1
:
xn-1 yn-1
The first integer n is the number of points.
In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.
Output
Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.
Examples
Input
2
0.0 0.0
1.0 0.0
Output
1.000000
Input
3
0.0 0.0
2.0 0.0
1.0 1.0
Output
1.41421356237
Submitted Solution:
```
import sys
file_input = sys.stdin
n = file_input.readline()
def distance(s_p1, s_p2):
x1, y1 = map(float, s_p1.split())
x2, y2 = map(float, s_p2.split())
return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5
import itertools
min_d = 400
for p1, p2 in itertools.combinations(file_input, 2):
min_d = min(min_d, distance(p1, p2))
print('{:f}'.format(min_d))
``` | instruction | 0 | 71,611 | 5 | 143,222 |
No | output | 1 | 71,611 | 5 | 143,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given an integer $n$, print all permutations of $\\{1, 2, ..., n\\}$ in lexicographic order.
Constraints
* $1 \leq n \leq 9$
Input
An integer $n$ is given in a line.
Output
Print each permutation in a line in order. Separate adjacency elements by a space character.
Examples
Input
2
Output
1 2
2 1
Input
3
Output
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Submitted Solution:
```
import itertools
[print(" ".join(list(map(str, x)))) for x in itertools.permutations(range(1,int(input())+1))]
``` | instruction | 0 | 71,621 | 5 | 143,242 |
Yes | output | 1 | 71,621 | 5 | 143,243 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given an integer $n$, print all permutations of $\\{1, 2, ..., n\\}$ in lexicographic order.
Constraints
* $1 \leq n \leq 9$
Input
An integer $n$ is given in a line.
Output
Print each permutation in a line in order. Separate adjacency elements by a space character.
Examples
Input
2
Output
1 2
2 1
Input
3
Output
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Submitted Solution:
```
def permutations(n):
"""Yields all permutations of {1, 2, ... , n}
>>> list(permutations(2))
[[1, 2], [2, 1]]
>>> list(permutations(3))
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
"""
xs = list(range(1, n+1))
yield xs[:]
while True:
i = n - 1
while i > 0 and xs[i-1] > xs[i]:
i -= 1
if i > 0:
i -= 1
j = i + 1
while j < len(xs) and xs[j] > xs[i]:
j += 1
xs[i], xs[j-1] = xs[j-1], xs[i]
xs = xs[:i+1] + list(reversed(xs[i+1:]))
yield xs[:]
else:
break
def run():
n = int(input())
for ps in permutations(n):
print(" ".join([str(x) for x in ps]))
if __name__ == '__main__':
run()
``` | instruction | 0 | 71,622 | 5 | 143,244 |
Yes | output | 1 | 71,622 | 5 | 143,245 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given an integer $n$, print all permutations of $\\{1, 2, ..., n\\}$ in lexicographic order.
Constraints
* $1 \leq n \leq 9$
Input
An integer $n$ is given in a line.
Output
Print each permutation in a line in order. Separate adjacency elements by a space character.
Examples
Input
2
Output
1 2
2 1
Input
3
Output
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Submitted Solution:
```
from itertools import permutations
n = int(input())
b = permutations(range(1, n+1))
for ele in b:
print(" ".join(map(str, ele)))
``` | instruction | 0 | 71,623 | 5 | 143,246 |
Yes | output | 1 | 71,623 | 5 | 143,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
n=int(input())
for i in range(0,n):
a,b=input().split(" ")
a,b=int(a),int(b)
print(a,a*2)
``` | instruction | 0 | 71,672 | 5 | 143,344 |
Yes | output | 1 | 71,672 | 5 | 143,345 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
for _ in range(int(input())):
l, r = map(int, input().split())
v = 2
while True:
ans = l * v
if ans <= r and (l is not ans):
print(l, ans)
break
elif ans > r:
l += 1
v = l
continue
v += 1
``` | instruction | 0 | 71,673 | 5 | 143,346 |
Yes | output | 1 | 71,673 | 5 | 143,347 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
t = int(input())
for i in range(0,t):
a = input().split()
x = int(a[0])
y = int(a[1])
z = int(y/x)
y = x*z;
ans = str(x) + " " + str(y)
print(ans)
``` | instruction | 0 | 71,674 | 5 | 143,348 |
Yes | output | 1 | 71,674 | 5 | 143,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
a=eval(input())
i=0
x=[]
while i<a:
x+=list(map(int,input().split()))
i+=1
ans=[]
i=0
b=0
while i<len(x)-1:
b=x[i+1]%x[i]
b=x[i+1]-b
ans+=[x[i]]+[b]
i+=2
i=0
while i <len(ans):
print(ans[i],ans[i+1])
i+=2
``` | instruction | 0 | 71,675 | 5 | 143,350 |
Yes | output | 1 | 71,675 | 5 | 143,351 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
for i in range(int(input())):
a,b=list(map(int,input().split()))
for j in range(a,b+1):
t=b//1
if j != j*(t-1):
print(j,j*(t-1))
break
``` | instruction | 0 | 71,676 | 5 | 143,352 |
No | output | 1 | 71,676 | 5 | 143,353 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
lines = int(input())
z = 0
answer = []
while z<lines:
numbers = input()
number = numbers.split()
number = list(map(int,number))
x = number[0]+1
y = number[1]-1
while y%x != 0 and y!=x and y>2*x:
y=y-1
if y%x!=0:
y = number[1]
while y%x != 0 and y != x:
x = x+1
a = 0
b = 1
answer.append(x)
answer.append(y)
a = a+2
b = b+2
z = z+1
z = 0
while z< len(answer):
print(""+str(answer[z])+" "+str(answer[z+1]))
z=z+2
``` | instruction | 0 | 71,677 | 5 | 143,354 |
No | output | 1 | 71,677 | 5 | 143,355 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
n = int(input())
for i in range(n):
l, r = map(int, (input().split()))
done = False
x = l
y = l + 1
while(not done):
for j in range(r - x):
if(not done):
if(y % x == 0):
done = True
else:
y += 1
x += 1
y = x + 1
print(x, y)
``` | instruction | 0 | 71,678 | 5 | 143,356 |
No | output | 1 | 71,678 | 5 | 143,357 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a range of positive integers from l to r.
Find such a pair of integers (x, y) that l ≤ x, y ≤ r, x ≠ y and x divides y.
If there are multiple answers, print any of them.
You are also asked to answer T independent queries.
Input
The first line contains a single integer T (1 ≤ T ≤ 1000) — the number of queries.
Each of the next T lines contains two integers l and r (1 ≤ l ≤ r ≤ 998244353) — inclusive borders of the range.
It is guaranteed that testset only includes queries, which have at least one suitable pair.
Output
Print T lines, each line should contain the answer — two integers x and y such that l ≤ x, y ≤ r, x ≠ y and x divides y. The answer in the i-th line should correspond to the i-th query from the input.
If there are multiple answers, print any of them.
Example
Input
3
1 10
3 14
1 10
Output
1 7
3 9
5 10
Submitted Solution:
```
n=int(input())
t=0
while t<n:
a=input().split()
x=int(a[0])
y=int(a[1])
print(str(x) + ' ' +str(y))
t+=1
``` | instruction | 0 | 71,679 | 5 | 143,358 |
No | output | 1 | 71,679 | 5 | 143,359 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0 | instruction | 0 | 71,952 | 5 | 143,904 |
Tags: bitmasks, dp, greedy, implementation, math
Correct Solution:
```
l,r=map(int,input().split())
s=bin(l)[2:]
t=bin(r)[2:]
z=max(len(s),len(t))
s='0'*(z-len(s))+s
t='0'*(z-len(t))+t
i=0
while i<z and s[i]==t[i]:
i=i+1
print(pow(2,z-i)-1)
``` | output | 1 | 71,952 | 5 | 143,905 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0 | instruction | 0 | 71,954 | 5 | 143,908 |
Tags: bitmasks, dp, greedy, implementation, math
Correct Solution:
```
l,r = map(int,input().split())
binR = list(bin(r)[2:])
binL = list((bin(l)[2:]).rjust(len(binR),"0"))
f,XOR,high,low = False,"","",""
for i,j in zip(binR,binL):
if i!=j:
if i=="1" and not f:f=True
high, low = high + i, low + j
XOR+="1"
if i==j:
if f:
high, low = high + "0", low + "1"
XOR+="1"
else:
high, low = high + i, low + i
XOR+="0"
print(int(XOR,2))
``` | output | 1 | 71,954 | 5 | 143,909 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
l,r = map(int,input().split())
p = l
lp = -1
while p:
p = p>>1
lp+=1
q = r
rp = -1
while q:
q = q>>1
rp+=1
s = max(lp,rp)
n=0
while s>=0:
if l>>s&1!=r>>s&1:
n |= (r>>s&1)<<s
break
s-=1
s-=1
while s>=0:
n |= 1<<s
s-=1
print(n)
``` | instruction | 0 | 71,959 | 5 | 143,918 |
Yes | output | 1 | 71,959 | 5 | 143,919 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
from sys import stdin,stdout
from collections import defaultdict,Counter
from bisect import bisect,bisect_left
import math
#stdin = open('input.txt','r')
I = stdin.readline
l,r = map(int,I().split())
def f(l,r):
ans = 0
f = 0
s = 0
for i in range(l,r+1):
for j in range(l,r+1):
now = i^j
if(now>ans):
ans = now
f = i
s = j
print(ans,r-l,l,r)
n = len(bin(r)[2:])
print(l,r,f,s)
print(bin(l)[2:],bin(r)[2:])
print(bin(f)[2:],bin(s)[2:])
print(bin(ans)[2:])
a = bin(l)[2:]
b = bin(r)[2:]
#f(l,r)
if(len(b)>len(a)):
le = len(b)
print(2**(math.floor(math.log(r,2))+1)-1)
#f(l,r)
else:
n = len(b)
diff = r-l
ans = ["1" for i in range(n)]
for i in range(n):
if(a[i] == "0" and b[i] == "1"):
pass
elif(a[i] == "1" and b[i] == "0"):
pass
else:
po = 2**(n-1-i)
if(po>diff):
#print(i,"this is i")
ans[i] = "0"
print(int("".join(ans),2))
``` | instruction | 0 | 71,960 | 5 | 143,920 |
Yes | output | 1 | 71,960 | 5 | 143,921 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
a, b = input().split()
a = int(a)
b = int(b)
s = a ^ b
cnt = 0
while s != 0:
s = int(s / 2)
cnt = cnt + 1
print((2 ** cnt) - 1)
``` | instruction | 0 | 71,961 | 5 | 143,922 |
Yes | output | 1 | 71,961 | 5 | 143,923 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
ii=lambda:int(input())
kk=lambda:map(int, input().split())
ll=lambda:list(kk())
from math import log
l,r=kk()
i=msb = int(max(log(l,2),log(r,2)))
while ((2**i)&l) == ((2**i)&r):
i-=1
if i == -1:
break
i+=1
print(2**i-1)
``` | instruction | 0 | 71,962 | 5 | 143,924 |
Yes | output | 1 | 71,962 | 5 | 143,925 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
arra = []
arrb = []
s = ""
temp = 1
value = 0
def Engine(num):
if num > 1:
Engine(num // 2)
arra.append( num%2 )
a,b = map(int,input().split())
Engine(b)
for i in range(len(arra)):
s += "1"
s = list(s)
for i in range(len(s)):
digit = s.pop()
if digit == '1':
value = value + pow(2, i)
print(value)
``` | instruction | 0 | 71,963 | 5 | 143,926 |
No | output | 1 | 71,963 | 5 | 143,927 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
import bisect
import sys
input=sys.stdin.readline
#t=int(input())
import collections
import heapq
t=1
p=10**9+7
def ncr_util():
inv[0]=inv[1]=1
fact[0]=fact[1]=1
for i in range(2,300001):
inv[i]=(inv[i%p]*(p-p//i))%p
for i in range(1,300001):
inv[i]=(inv[i-1]*inv[i])%p
fact[i]=(fact[i-1]*i)%p
def solve():
ans,a,b=0,0,0
mul=2**60
for i in range(60,-1,-1):
#print(mul,a+mul,b+mul)
if a+mul*2-1==l and b+mul*2-1==l and a<l and b<l:
#print(a,b,mul)
a+=mul
b+=mul
else:
if a+mul<=r:
#print(1,mul)
ans+=mul
a+=mul
elif b+mul<=r:
#print(2,mul)
ans+=mul
b+=mul
mul//=2
return ans
for _ in range(t):
#n=int(input())
#s=input()
#n=int(input())
#h,n=(map(int,input().split()))
#n1=n
#x=int(input())
#b=int(input())
#n,m,k=map(int,input().split())
#l=list(map(int,input().split()))
l,r=map(int,input().split())
#n=int(input())
#s=input()
#s1=input()
#p=input()
#l=list(map(int,input().split()))
#l.sort(revrese=True)
#l2=list(map(int,input().split()))
#l=str(n)
#l.sort(reverse=True)
#l2.sort(reverse=True)
#l1.sort(reverse=True)
print(solve())
``` | instruction | 0 | 71,964 | 5 | 143,928 |
No | output | 1 | 71,964 | 5 | 143,929 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
l,r=map(int,input().split())
a=2**(len(bin(r))-3)
if l==r:
exit(print(0))
if a>l:
print(2*a-1)
else:
m=a
n=a;b=1
while m<r:
m+=(a//2)
a//=2
while n<r:
n+=b
b*=2
print((m-a)^(n))
``` | instruction | 0 | 71,965 | 5 | 143,930 |
No | output | 1 | 71,965 | 5 | 143,931 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0
Submitted Solution:
```
import sys
# from math import log2,floor,ceil,sqrt
# import bisect
# from collections import deque
# from types import GeneratorType
# def bootstrap(func, stack=[]):
# def wrapped_function(*args, **kwargs):
# if stack:
# return func(*args, **kwargs)
# else:
# call = func(*args, **kwargs)
# while True:
# if type(call) is GeneratorType:
# stack.append(call)
# call = next(call)
# else:
# stack.pop()
# if not stack:
# break
# call = stack[-1].send(call)
# return call
# return wrapped_function
Ri = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10**8
N = 5*10**6
def solve(n):
arr = []
while n> 0:
arr.append(n%2)
n=n//2
return arr
l,r = Ri()
arrl = solve(l)
arrr = solve(r)
if len(arrr) > len(arrl):
ans = (1<<len(arrr))-1
print(ans)
else:
ans = (1<<(len(arrr)-1))-1
print(ans)
``` | instruction | 0 | 71,966 | 5 | 143,932 |
No | output | 1 | 71,966 | 5 | 143,933 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024
Submitted Solution:
```
n=int(input())
if n%2==0:
print(0)
else:
print(1)
``` | instruction | 0 | 72,113 | 5 | 144,226 |
Yes | output | 1 | 72,113 | 5 | 144,227 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024
Submitted Solution:
```
i = int(input())
if i <= 12 :
l = 2 ** i
else:
l = 2 ** i - 2 ** (i - 13) * 100
print(l)
``` | instruction | 0 | 72,114 | 5 | 144,228 |
Yes | output | 1 | 72,114 | 5 | 144,229 |
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