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.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
import sys
input = sys.stdin.readline
N, K = map(int, input().split())
A = [int(i) for i in input().split()]
p = []
m = []
zero = 0
for i in range(N) :
if A[i] > 0 :
p.append(A[i])
elif A[i] < 0 :
m.append(-A[i])
else :
zero += 1
p.sort()
m.sort()
ng, ok = -(10 ** 18)-1, 10 ** 18+1
while ok - ng > 1 :
mid = (ok + ng) // 2
s = 0
if mid < 0 :
j = 0
for i in range(len(m) - 1, -1, -1) :
while j < len(p) and m[i] * p[j] < -mid :
j += 1
s += len(p) - j
else :
j = len(p) - 1
for i in range(len(p)) :
while j >= 0 and p[i] * p[j] > mid :
j -= 1
s += max(0, j - i)
j = len(m) - 1
for i in range(len(m)) :
while j >= 0 and m[i] * m[j] > mid :
j -= 1
s += max(0, j - i)
s += (len(p) + len(m)) * zero + len(p) * len(m) + zero * (zero - 1) // 2
if s < K :
ng = mid
else :
ok = mid
print(ok)
``` | instruction | 0 | 13,932 | 5 | 27,864 |
Yes | output | 1 | 13,932 | 5 | 27,865 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
N,K = map(int,input().split())
A = list(map(int,input().split()))
A = sorted(A)
mi = 0
zero = 0
for a in A:
if a<0:
mi+=1
elif a==0:
zero+=1
else:
break
plu = N-mi-zero
A_mi = A[0:mi:]
A_mi_rev = A_mi[::-1]
A_plu = A[mi+zero::]
A_plu_rev = A_plu[::-1]
num_mi = plu*mi
num_zero = (plu+mi)*zero+(zero*(zero-1))//2
r = max(A[-1]**2+10,A[0]**2+10)
l = A[0]*A[-1]-10
while l+1!=r:
m = (l+r)//2
num = 0
if m>0:
num+=num_mi+num_zero
if num>=K:
r=m
continue
cou=0
for i in range(0,plu):
while True:
if cou>=plu-i-1:
num+=plu-i-1
break
x = A_plu_rev[i]*A_plu[cou]
if x<m:
cou+=1
else:
num+=cou
break
if num>=K:
break
if num>=K:
r=m
continue
cou = 0
for i in range(0,mi):
while True:
if cou>=mi-i-1:
num+=mi-i-1
break
x = A_mi[i]*A_mi_rev[cou]
if x<m:
cou+=1
else:
num+=cou
break
if num>=K:
break
if num>=K:
r=m
else:
l=m
elif m==0:
num+=num_mi
if num>=K:
r=m
else:
l=m
else:
cou = 0
for a in A_mi_rev:
while True:
if cou==plu:
num+=cou
break
x = a*A_plu_rev[cou]
if x<m:
cou+=1
else:
num+=cou
break
if num>=K:
break
if num>=K:
r = m
else:
l = m
print(l)
``` | instruction | 0 | 13,933 | 5 | 27,866 |
No | output | 1 | 13,933 | 5 | 27,867 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
import sys
from bisect import bisect_left
import numpy as np
from math import ceil
def main():
read = sys.stdin.read
N, K, *A = map(int, read().split())
A.sort()
m = bisect_left(A, 0)
z = bisect_left(A, 1) - m
p = N - m - z
M = m * p
Z = z * (N - z) + z * (z - 1) // 2
if K <= M:
left = A[0] * A[-1] - 1
right = 0
minuses = np.array(A[:m], np.int64)
pluses = np.array(A[-p:], np.int64)
while left + 1 < right:
mid = ceil((left + right) / 2)
a = (p - np.searchsorted(pluses, np.ceil(mid / minuses), side='left')).sum()
if a < K:
left = mid
else:
right = mid
print(right)
elif K <= M + Z:
print(0)
else:
print(1)
if __name__ == '__main__':
main()
``` | instruction | 0 | 13,934 | 5 | 27,868 |
No | output | 1 | 13,934 | 5 | 27,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
import bisect
n,k=map(int,input().split())
A=list(map(int,input().split()))
A.sort()
x=bisect.bisect_left(A,0,lo=0,hi=len(A))
y=bisect.bisect_right(A,0,lo=0,hi=len(A))
AN=x
A0=y-x
AP=n-y
if x!=0:
An=A[:x]
else:
An=[]
Ann=An[::-1]
Annn=[0]*AN
for i in range(AN):
Annn[i]=Ann[i]*(-1)
if y!=n:
App=A[-n+y:]
Ap=App[::-1]
else:
Ap=[]
if k<=AN*AP:
ok=An[0]*Ap[0]-1
ng=0
while ng-ok>1:
mid=(ok+ng)//2
c=0
for i in range(AN):
c=c+AP-bisect.bisect_left(App,((-1)*mid+(-1)*An[i]-1)//((-1)*An[i]),lo=0,hi=AP)
if c<k:
ok=mid
else:
ng=mid
ans=ok+1
print(ans)
elif k<=n*(n-1)//2-AN*(AN-1)//2-AP*(AP-1)//2:
print(0)
else:
k=n*(n-1)//2-k+1
if AN>0 and AP>0:
ok=max(An[0]**2,Ap[0]**2)
elif AN>0:
ok=An[0]**2
else:
ok=Ap[0]**2
ng=0
while ok-ng>1:
mid=(ok+ng)//2
c=0
for i in range(AN):
c=c+max(0,AN-i-1-bisect.bisect_left(Annn,(mid+Annn[AN-i-1]-1)//Annn[AN-i-1],lo=0,hi=AN))
for i in range(AP):
c=c+max(0,AP-i-1-bisect.bisect_left(App,(mid+App[AP-i-1]-1)//App[AP-i-1],lo=0,hi=AP))
if c<k:
ok=mid
else:
ng=mid
ans=ok-1
print(ans)
``` | instruction | 0 | 13,935 | 5 | 27,870 |
No | output | 1 | 13,935 | 5 | 27,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
n,k = map(int,input().split())
a = list(map(int,input().split()))
a.sort()
p = []
z = []
m = []
for i in range(n):
if a[i] > 0:
p.append(a[i])
elif a[i] == 0:
z.append(a[i])
else:
m.append(a[i])
nb1 = a[0]*a[n-1]
nb2 = max(a[0]*a[1],a[n-1]*a[n-2])
p1 = len(p)
z1 = len(z)
m1 = len(m)
#print(p,m)
#print(p1,z1,m1)
def sytr(x,p,z,m,p1,z1,m1):
ans = 0
ans2 = 0
ans3 = -10**18
if x > 0:
m.sort(reverse=True)
p.sort()
ans += p1*m1 + (p1+m1)*z1 + (z1-1)*z1//2
ans2 += ans
now = 0
#print(p)
now1 = p1-1
now2 = 0
now3 = p1-1
if p1 > 1:
while now < now1:
if p[now]*p[now1] > x:
now1 -= 1
else:
ans3 = max(ans3,p[now]*p[now1])
ans += now1-now
now += 1
while now2 < now3:
if p[now2]*p[now3] >= x:
now3 -= 1
else:
ans2 += now3 - now2
now2 += 1
if m1 > 1:
now = 0
now1 = m1-1
now2 = 0
now3 = m1-1
while now < now1:
if m[now]*m[now1] > x:
now1 -= 1
else:
ans3 = max(ans3,m[now]*m[now1])
ans += now1 - now
now += 1
while now2 < now3:
if m[now2]*m[now3] >= x:
now3 -= 1
else:
ans2 += now3 - now2
now2 += 1
elif x == 0:
p.sort()
m.sort()
if p1 > 0 and m1 > 0:
ans3 = p[0]*m[m1-1]
if z1 > 0:
ans3 = 0
ans += p1*m1
ans2 += (p1+m1)*z1 + ans
else:
p.sort(reverse=True)
m.sort()
now = 0
now1 = m1-1
now2 = 0
now3 = m1-1
if p1 > 0 and m1 > 0:
while now < p1 and now1 >= 0:
if p[now]*m[now1] > x:
now1 -= 1
else:
ans3 = max(ans3,p[now]*m[now1])
ans += now1+1
now += 1
while now2 < p1 and now3 >= 0:
if p[now2]*m[now3] >= x:
now3 -= 1
else:
ans2 += now3+1
now2 += 1
return [ans,ans2,ans3]
while nb1 + 1 < nb2:
#print(nb1,nb2)
x = (nb1+nb2)//2
#print(sytr(x,p,z,m,p1,z1,m1))
if max(sytr(x,p,z,m,p1,z1,m1)[0],sytr(x,p,z,m,p1,z1,m1)[1]) < k:
nb1 = x
elif min(sytr(x,p,z,m,p1,z1,m1)[0],sytr(x,p,z,m,p1,z1,m1)[1]) > k:
nb2 = x
else:
if abs(sytr(x,p,z,m,p1,z1,m1)[1]-sytr(x,p,z,m,p1,z1,m1)[0]) == 0:
x = sytr(x,p,z,m,p1,z1,m1)[2]
break
else:
break
print(x)
``` | instruction | 0 | 13,936 | 5 | 27,872 |
No | output | 1 | 13,936 | 5 | 27,873 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
Cards with ranks of $ 2 $ and $ 8 $ are powerful in card game millionaires. Therefore, we call an integer consisting of only the numbers $ 2 $ and $ 8 $ in $ 10 $ decimal notation a good integer. The best integers are listed from the smallest to $ 2, 8, 22, 28, 82, 88, \ cdots $.
Let $ n $ be a positive integer. When $ n $ can be expressed in the form of a product of good integers, find the maximum product. If you can't, output $ -1 $.
Constraint
$ 1 \ leq n \ leq 10 ^ {18} $
sample
Sample input 1
1
Sample output 1
-1
Sample input 2
2
Sample output 2
1
Sample input 3
88
Sample output 3
3
It can be expressed as $ 2 \ times 2 \ times 22 $.
Sample input 4
100
Sample output 4
-1
Sample input 5
173553147234869248
Sample output 5
11
It can be expressed as $ 2 ^ 6 \ times 28 \ times 2222 ^ 3 \ times 8828 $.
input
$ n $
output
Print the answer on the $ 1 $ line.
Example
Input
1
Output
-1 | instruction | 0 | 14,102 | 5 | 28,204 |
"Correct Solution:
```
import bisect
import sys
sys.setrecursionlimit(10000)
a=[]
def f(a,bin,n):
if bin>n:return
if bin:a+=[bin]
f(a,bin*10+2,n)
f(a,bin*10+8,n)
def g(n,p):
m=-1<<20
x=bisect.bisect_left(a,n)
if x!=len(a) and a[x]==n:m=1
if a[p]**2>n:return m
if n%a[p]==0:m=g(n//a[p],p)+1
return max(m,g(n,p+1))
n=int(input())
if n&1:print(-1);exit()
f(a,0,n)
a=sorted(a)
b=g(n,0)
if b<0:b=-1
print(b)
``` | output | 1 | 14,102 | 5 | 28,205 |
Provide a correct Python 3 solution for this coding contest problem.
Problem statement
Cards with ranks of $ 2 $ and $ 8 $ are powerful in card game millionaires. Therefore, we call an integer consisting of only the numbers $ 2 $ and $ 8 $ in $ 10 $ decimal notation a good integer. The best integers are listed from the smallest to $ 2, 8, 22, 28, 82, 88, \ cdots $.
Let $ n $ be a positive integer. When $ n $ can be expressed in the form of a product of good integers, find the maximum product. If you can't, output $ -1 $.
Constraint
$ 1 \ leq n \ leq 10 ^ {18} $
sample
Sample input 1
1
Sample output 1
-1
Sample input 2
2
Sample output 2
1
Sample input 3
88
Sample output 3
3
It can be expressed as $ 2 \ times 2 \ times 22 $.
Sample input 4
100
Sample output 4
-1
Sample input 5
173553147234869248
Sample output 5
11
It can be expressed as $ 2 ^ 6 \ times 28 \ times 2222 ^ 3 \ times 8828 $.
input
$ n $
output
Print the answer on the $ 1 $ line.
Example
Input
1
Output
-1 | instruction | 0 | 14,103 | 5 | 28,206 |
"Correct Solution:
```
import bisect
import sys
sys.setrecursionlimit(10000)
a=[]
def f(a,bin,n):
if bin>n:return
if bin:a+=[bin]
f(a,bin*10+2,n)
f(a,bin*10+8,n)
def g(n,p):
m=-1<<20
x=bisect.bisect_left(a,n)
if x!=len(a) and a[x]==n:m=1
if a[p]**2>n:return m
if n%a[p]==0:m=g(n//a[p],p)+1
return max(m,g(n,p+1))
n=int(input())
if n&1:print(-1);exit()
f(a,0,n)
a=sorted(a)+[10**20]
b=g(n,0)
if b<0:b=-1
print(b)
``` | output | 1 | 14,103 | 5 | 28,207 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem statement
Cards with ranks of $ 2 $ and $ 8 $ are powerful in card game millionaires. Therefore, we call an integer consisting of only the numbers $ 2 $ and $ 8 $ in $ 10 $ decimal notation a good integer. The best integers are listed from the smallest to $ 2, 8, 22, 28, 82, 88, \ cdots $.
Let $ n $ be a positive integer. When $ n $ can be expressed in the form of a product of good integers, find the maximum product. If you can't, output $ -1 $.
Constraint
$ 1 \ leq n \ leq 10 ^ {18} $
sample
Sample input 1
1
Sample output 1
-1
Sample input 2
2
Sample output 2
1
Sample input 3
88
Sample output 3
3
It can be expressed as $ 2 \ times 2 \ times 22 $.
Sample input 4
100
Sample output 4
-1
Sample input 5
173553147234869248
Sample output 5
11
It can be expressed as $ 2 ^ 6 \ times 28 \ times 2222 ^ 3 \ times 8828 $.
input
$ n $
output
Print the answer on the $ 1 $ line.
Example
Input
1
Output
-1
Submitted Solution:
```
import bisect
a=[]
def f(a,bin,n):
if bin>n:return
if bin:a+=[bin]
f(a,bin*10+2,n)
f(a,bin*10+8,n)
def g(n,p):
m=-1<<20
x=bisect.bisect_left(a,n)
if p>len(a):return m
if x!=len(a) and a[x]==n:m=1
if a[p]**2>n:return m
if n%a[p]==0:m=g(n//a[p],p)+1
return max(m,g(n,p+1))
n=int(input())
if n&1:print(-1);exit()
f(a,0,n)
a=sorted(a)+[10**20]
b=g(n,0)
if b<0:b=-1
print(b)
``` | instruction | 0 | 14,104 | 5 | 28,208 |
No | output | 1 | 14,104 | 5 | 28,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem statement
Cards with ranks of $ 2 $ and $ 8 $ are powerful in card game millionaires. Therefore, we call an integer consisting of only the numbers $ 2 $ and $ 8 $ in $ 10 $ decimal notation a good integer. The best integers are listed from the smallest to $ 2, 8, 22, 28, 82, 88, \ cdots $.
Let $ n $ be a positive integer. When $ n $ can be expressed in the form of a product of good integers, find the maximum product. If you can't, output $ -1 $.
Constraint
$ 1 \ leq n \ leq 10 ^ {18} $
sample
Sample input 1
1
Sample output 1
-1
Sample input 2
2
Sample output 2
1
Sample input 3
88
Sample output 3
3
It can be expressed as $ 2 \ times 2 \ times 22 $.
Sample input 4
100
Sample output 4
-1
Sample input 5
173553147234869248
Sample output 5
11
It can be expressed as $ 2 ^ 6 \ times 28 \ times 2222 ^ 3 \ times 8828 $.
input
$ n $
output
Print the answer on the $ 1 $ line.
Example
Input
1
Output
-1
Submitted Solution:
```
import bisect
a=[]
def f(a,bin,n):
if bin>n:return
if bin:a+=[bin]
f(a,bin*10+2,n)
f(a,bin*10+8,n)
def g(n,p):
m=-1<<20
x=bisect.bisect_left(a,n)
if x!=len(a) and a[x]==n:m=1
if a[p]**2>n:return m
if n%a[p]==0:m=g(n//a[p],p)+1
return max(m,g(n,p+1))
n=int(input())
if n&1:print(-1);exit()
f(a,0,n)
a.sort()
b=g(n,0)
if b<0:b=-1
print(b)
``` | instruction | 0 | 14,105 | 5 | 28,210 |
No | output | 1 | 14,105 | 5 | 28,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem statement
Cards with ranks of $ 2 $ and $ 8 $ are powerful in card game millionaires. Therefore, we call an integer consisting of only the numbers $ 2 $ and $ 8 $ in $ 10 $ decimal notation a good integer. The best integers are listed from the smallest to $ 2, 8, 22, 28, 82, 88, \ cdots $.
Let $ n $ be a positive integer. When $ n $ can be expressed in the form of a product of good integers, find the maximum product. If you can't, output $ -1 $.
Constraint
$ 1 \ leq n \ leq 10 ^ {18} $
sample
Sample input 1
1
Sample output 1
-1
Sample input 2
2
Sample output 2
1
Sample input 3
88
Sample output 3
3
It can be expressed as $ 2 \ times 2 \ times 22 $.
Sample input 4
100
Sample output 4
-1
Sample input 5
173553147234869248
Sample output 5
11
It can be expressed as $ 2 ^ 6 \ times 28 \ times 2222 ^ 3 \ times 8828 $.
input
$ n $
output
Print the answer on the $ 1 $ line.
Example
Input
1
Output
-1
Submitted Solution:
```
import bisect
a=[]
def f(n,p):
m=-1<<20
x=bisect.bisect_left(a,n)
if a[x]==n:m=1
if a[p]**2>n:return m
if n%a[p]==0:m=f(n//a[p],p)+1
return max(m,f(n,p+1))
for i in range(1,19):
for j in range(1<<i):
b=''
for k in range(i):
if (j//(1<<k))%2:b+='2'
else:b+='8'
a+=[int(b)]
a.sort()
n=int(input())
b=f(n,0)
if n==1 or b<0:b=-1
print(b)
``` | instruction | 0 | 14,106 | 5 | 28,212 |
No | output | 1 | 14,106 | 5 | 28,213 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $
Input
The input is given in the following format.
$ a $ $ b $ $ x $
Three integers $ a $, $ b $, $ x $ are given, separated by spaces.
Output
Print the answer on one line.
Examples
Input
3 1 5
Output
7
Input
3 2 5
Output
11
Input
82 69 64
Output
64
Input
316250877917604 316250877917599 681260158257385
Output
62687552 | instruction | 0 | 14,108 | 5 | 28,216 |
"Correct Solution:
```
a, b, x = map(int, input().split())
print((x+max(0, x-b)//(a-b)*b)%1000000007)
``` | output | 1 | 14,108 | 5 | 28,217 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $
Input
The input is given in the following format.
$ a $ $ b $ $ x $
Three integers $ a $, $ b $, $ x $ are given, separated by spaces.
Output
Print the answer on one line.
Examples
Input
3 1 5
Output
7
Input
3 2 5
Output
11
Input
82 69 64
Output
64
Input
316250877917604 316250877917599 681260158257385
Output
62687552 | instruction | 0 | 14,109 | 5 | 28,218 |
"Correct Solution:
```
def inpl(): return list(map(int, input().split()))
MOD = 10**9 + 7
a, b, x = inpl()
if x < a:
print(x%MOD)
else:
e = (x-b)//(a-b)
print((x + e*b)%MOD)
``` | output | 1 | 14,109 | 5 | 28,219 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $
Input
The input is given in the following format.
$ a $ $ b $ $ x $
Three integers $ a $, $ b $, $ x $ are given, separated by spaces.
Output
Print the answer on one line.
Examples
Input
3 1 5
Output
7
Input
3 2 5
Output
11
Input
82 69 64
Output
64
Input
316250877917604 316250877917599 681260158257385
Output
62687552 | instruction | 0 | 14,110 | 5 | 28,220 |
"Correct Solution:
```
a,b,x = [int(i) for i in input().split()]
d = a - b
n = max(0,(x - b)) // d
ans = x + n * b
print(ans % 1000000007)
``` | output | 1 | 14,110 | 5 | 28,221 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $
Input
The input is given in the following format.
$ a $ $ b $ $ x $
Three integers $ a $, $ b $, $ x $ are given, separated by spaces.
Output
Print the answer on one line.
Examples
Input
3 1 5
Output
7
Input
3 2 5
Output
11
Input
82 69 64
Output
64
Input
316250877917604 316250877917599 681260158257385
Output
62687552 | instruction | 0 | 14,111 | 5 | 28,222 |
"Correct Solution:
```
a, b, x = [int(k) for k in input().split()]
if x >= a:
d = ((x-b) // (a-b))* b + x
else:
d = x
print(d%1000000007)
``` | output | 1 | 14,111 | 5 | 28,223 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $
Input
The input is given in the following format.
$ a $ $ b $ $ x $
Three integers $ a $, $ b $, $ x $ are given, separated by spaces.
Output
Print the answer on one line.
Examples
Input
3 1 5
Output
7
Input
3 2 5
Output
11
Input
82 69 64
Output
64
Input
316250877917604 316250877917599 681260158257385
Output
62687552 | instruction | 0 | 14,112 | 5 | 28,224 |
"Correct Solution:
```
#!/usr/bin/env python3
a, b, x = map(int, input().split())
print((x + max(x - b, 0) // (a - b) * b) % 1000000007)
``` | output | 1 | 14,112 | 5 | 28,225 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $
Input
The input is given in the following format.
$ a $ $ b $ $ x $
Three integers $ a $, $ b $, $ x $ are given, separated by spaces.
Output
Print the answer on one line.
Examples
Input
3 1 5
Output
7
Input
3 2 5
Output
11
Input
82 69 64
Output
64
Input
316250877917604 316250877917599 681260158257385
Output
62687552 | instruction | 0 | 14,113 | 5 | 28,226 |
"Correct Solution:
```
#! /usr/bin/env python3
a, b, x = map(int, input().split())
MOD = int(1e9+7)
if x < a:
res = x % MOD
else:
k = (x-b) // (a-b)
res = (x + b*k)
res %= MOD
print(res)
``` | output | 1 | 14,113 | 5 | 28,227 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,130 | 5 | 28,260 |
"Correct Solution:
```
class Node:
def __init__(self, value):
self.value = value
self.next = None
class List:
def __init__(self):
self.head = None
self.tail = None
def insert(self, v):
node = Node(v)
if self.tail is None:
self.head = node
self.tail = node
else:
self.tail.next = node
self.tail = node
def dump(self):
node = self.head
while node is not None:
yield node.value
node = node.next
def splice(self, li):
if self.head is None:
self.head = li.head
self.tail = li.tail
else:
self.tail.next = li.head
self.tail = li.tail
li.clear()
def clear(self):
self.head = None
self.tail = None
def run():
n, q = [int(x) for x in input().split()]
ls = [List() for _ in range(n)]
for _ in range(q):
com = [int(x) for x in input().split()]
c = com[0]
if c == 0:
t, v = com[1:]
ls[t].insert(v)
elif c == 1:
t = com[1]
values = []
for v in ls[t].dump():
values.append(str(v))
print(" ".join(values))
elif c == 2:
s, t = com[1:]
ls[t].splice(ls[s])
else:
raise ValueError('invalid command')
if __name__ == '__main__':
run()
``` | output | 1 | 14,130 | 5 | 28,261 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,131 | 5 | 28,262 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
from collections import deque
N,Q = map(int,input().split())
L = [deque([]) for _ in range(N)]
for _ in range(Q):
q = list(map(int,input().split()))
if q[0] == 0:
L[q[1]].append(q[2])
elif q[0] == 1:
if L[q[1]]:
print(' '.join(map(str,L[q[1]])))
else:
print()
else:
if L[q[1]]:
if L[q[2]]:
if len(L[q[1]]) == 1:
L[q[2]].append(L[q[1]][0])
elif len(L[q[2]]) == 1:
L[q[1]].appendleft(L[q[2]][0])
L[q[2]] = L[q[1]]
else:
L[q[2]].extend(L[q[1]])
else:
L[q[2]] = L[q[1]]
L[q[1]] = deque([])
``` | output | 1 | 14,131 | 5 | 28,263 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,132 | 5 | 28,264 |
"Correct Solution:
```
import collections
class Splice():
def __init__(self, num_lists):
self.lists = [collections.deque() for i in range(0, num_lists, 1)]
def insert(self, t, x):
self.lists[t].append(x)
return self
def dump(self, t):
print(' '.join(map(str, self.lists[t])))
def splice(self, s, t):
if self.lists[t]:
if len(self.lists[s]) == 1:
self.lists[t].append(self.lists[s][0])
elif len(self.lists[t]) == 1:
self.lists[s].appendleft(self.lists[t][0])
self.lists[t] = self.lists[s]
else:
self.lists[t].extend(self.lists[s])
else:
self.lists[t] = self.lists[s]
self.lists[s] = collections.deque()
return self
num_lists, num_op = map(int, input().split(' '))
lists = Splice(num_lists)
for op in range(0, num_op):
op = tuple(map(int, input().split(' ')))
if op[0] == 0:
lists.insert(op[1], op[2])
elif op[0] == 1:
lists.dump(op[1])
elif op[0] == 2:
lists.splice(op[1], op[2])
``` | output | 1 | 14,132 | 5 | 28,265 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,133 | 5 | 28,266 |
"Correct Solution:
```
import sys
from collections import deque,defaultdict
A = defaultdict(deque)
sys.stdin.readline().split()
ans =[]
for query in sys.stdin:
if query[0] == "0":
t,x = query[2:].split()
A[t].append(x)
elif query[0] == "1":
ans.append(" ".join(A[query[2:-1]]) + "\n")
else:
s,t = query[2:].split()
if A[t]:
if len(A[s]) == 1:
A[t].append(A[s][0])
elif len(A[t]) == 1:
A[s].appendleft(A[t][0])
A[t] = A[s]
else:
A[t].extend(A[s])
else:
A[t] = A[s]
A[s] = deque()
sys.stdout.writelines(ans)
``` | output | 1 | 14,133 | 5 | 28,267 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,134 | 5 | 28,268 |
"Correct Solution:
```
def solve():
from collections import deque
from sys import stdin
f_i = stdin
n, q = map(int, f_i.readline().split())
L = [deque() for i in range(n)]
ans = []
for op in (line.split() for line in f_i):
op_type = op[0]
if op_type == '0':
L[int(op[1])].append(op[2])
elif op_type == '1':
ans.append(' '.join(L[int(op[1])]))
else:
s = int(op[1])
ls = L[s]
t = int(op[2])
lt = L[t]
if lt:
if len(ls) == 1:
lt.append(ls[0])
elif len(lt) == 1:
ls.appendleft(lt[0])
L[t] = ls
elif ls:
lt.extend(ls)
else:
L[t] = ls
L[s] = deque()
print('\n'.join(ans))
solve()
``` | output | 1 | 14,134 | 5 | 28,269 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,135 | 5 | 28,270 |
"Correct Solution:
```
from collections import deque
import sys
n, q = map(int, input().split())
# Q = [[] for _ in range(n)]
Q = [deque() for _ in range(n)]
ans = []
for query in (line.split() for line in sys.stdin):
s = int(query[1])
if query[0] == '0':
t = int(query[2])
Q[s].append(t)
elif query[0] == '1':
# ans.append(Q[s])
print(*Q[s])
elif query[0] == '2':
t = int(query[2])
if Q[t]:
if len(Q[s]) == 1:
Q[t].append(Q[s][0])
elif len(Q[t]) == 1:
Q[s].appendleft(Q[t][0])
Q[t] = Q[s]
else:
Q[t].extend(Q[s])
else:
Q[t] = Q[s]
Q[s] = deque()
# for i in ans:
# print(i)
``` | output | 1 | 14,135 | 5 | 28,271 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,136 | 5 | 28,272 |
"Correct Solution:
```
import sys
from collections import deque
sys.setrecursionlimit(10**9)
n,q = map(int, input().split())
l = [deque() for _ in range(n)]
for _ in range(q):
query = input().split()
if query[0] == "0": # insert
idx = int(query[1])
l[idx].append(query[2])
elif query[0] == "1": # dump
idx = int(query[1])
print(" ".join(l[idx]))
elif query[0] == "2": # splice
idx1 = int(query[1])
idx2 = int(query[2])
if len(l[idx1]) > 1:
if len(l[idx2]) == 0:
l[idx2] = l[idx1]
elif len(l[idx2]) == 1:
l[idx1].appendleft(l[idx2][0])
l[idx2] = l[idx1]
else:
l[idx2].extend(l[idx1])
elif len(l[idx1]) == 1:
l[idx2].append(l[idx1][0])
l[idx1] = deque()
``` | output | 1 | 14,136 | 5 | 28,273 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6 | instruction | 0 | 14,137 | 5 | 28,274 |
"Correct Solution:
```
from collections import deque
n, q = [int(x) for x in input().split()]
L = [ deque() for _ in range(n) ]
for _ in range(q):
c, t, x = [int(x) for x in (input()+" 0").split()][:3]
if c == 0:
L[t].append(x)
elif c == 1:
print( " ".join(map(str,L[t])))
else:
s,t = t, x
if L[s]:
if L[t]:
if len(L[s]) == 1:
L[t].append(L[s][0])
elif len(L[t]) == 1:
L[s].appendleft(L[t][0])
L[t] = L[s]
else:
L[t].extend(L[s])
else:
L[t] = L[s]
L[s] = deque()
``` | output | 1 | 14,137 | 5 | 28,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
from collections import deque
def insert(t, x):
Llist[t].append(x)
def dump(t):
print(*Llist[t])
def splice(s, t):
if Llist[t]:
if len(Llist[t]) ==1:
Llist[s].appendleft(Llist[t][0])
Llist[t] = Llist[s]
elif len(Llist[s]) == 1:
Llist[t].append(Llist[s][0])
else:
Llist[t].extend(Llist[s])
else:
Llist[t] = Llist[s]
Llist[s] = deque()
n, q = map(int, input().split())
Llist = []
for i in range(n):
Llist.append(deque())
for i in range(q):
queryi = list(map(int, input().split()))
if queryi[0] == 0:
insert(queryi[1], queryi[2])
elif queryi[0] == 1:
dump(queryi[1])
else:
splice(queryi[1], queryi[2])
``` | instruction | 0 | 14,138 | 5 | 28,276 |
Yes | output | 1 | 14,138 | 5 | 28,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
from sys import stdin,stdout
from collections import defaultdict,deque
n, q = map(int,stdin.readline().split())
queries = stdin.readlines()
A = defaultdict(deque)
ans = []
#count = 0
for query in queries:
#print(count)
#count += 1
query = query.split()
if query[0] == '0':
A[int(query[1])].append(query[2])
elif query[0] == '1':
ans.append(' '.join(A[int(query[1])]) + '\n')
else:
s = int(query[1])
t = int(query[2])
if (A[t]):
if len(A[s]) == 1:
A[t].append(A[s][0])
elif len(A[t]) == 1:
A[s].appendleft(A[t][0])
A[t] = A[s]
else:
A[t].extend(A[s])
else:
A[t] = A[s]
A[s] = deque()
stdout.writelines(ans)
``` | instruction | 0 | 14,139 | 5 | 28,278 |
Yes | output | 1 | 14,139 | 5 | 28,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
from collections import deque
import sys
sys.setrecursionlimit(10**9)
def input():
return sys.stdin.readline().strip()
n,q = map(int,input().split())
L = deque(deque() for i in range(n))
for i in range(q):
query = input().split()
if query[0] == "0":
L[int(query[1])].append(query[2])
elif query[0] == "1":
print(" ".join(L[int(query[1])]))
else:
s = int(query[1])
t = int(query[2])
if len(L[s]):
if len(L[t]) == 0:
L[t] = L[s]
elif len(L[t]) == 1:
L[s].appendleft(L[t][0])
L[t] = L[s]
else:
L[t].extend(L[s])
elif len(L[s]) == 1:
L[t].append(L[t][0])
L[s] = deque()
``` | instruction | 0 | 14,140 | 5 | 28,280 |
Yes | output | 1 | 14,140 | 5 | 28,281 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
from collections import deque
readline = open(0).readline
writelines = open(1, 'w').writelines
N, Q = map(int, readline().split())
ans = []
A = [deque() for i in range(N)]
def push(t, x):
A[t].append(str(x))
def dump(t):
ans.append(" ".join(A[t]))
ans.append("\n")
def splice(s, t):
if A[s]:
if A[t]:
if len(A[s]) == 1:
A[t].append(A[s][0])
elif len(A[t]) == 1:
A[s].appendleft(A[t][0])
A[t] = A[s]
else:
A[t].extend(A[s])
else:
A[t] = A[s]
A[s] = deque()
C = [push, dump, splice].__getitem__
for i in range(Q):
t, *a=map(int, readline().split())
C(t)(*a)
writelines(ans)
``` | instruction | 0 | 14,141 | 5 | 28,282 |
Yes | output | 1 | 14,141 | 5 | 28,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
flag = 0
def lsprint(lists):
global flag
if lists:
if flag:
print()
print()
else:
flag = 1
print(lists.pop(0), end = '')
for i in lists:
print(' %s' %i, end = '')
else:
pass
def splice(s, t):
return s + t, []
if __name__ == '__main__':
n, q = input().split()
n, q = int(n), int(q)
lists = [[] for _ in range(n)]
for i in range(q):
query = input().split()
if query[0] == "0":
lists[int(query[1])].insert(-1, query[2])
elif query[0] == "1":
lsprint(lists[int(query[1])])
else:
lists[int(query[1])], lists[int(query[2])] = splice(lists[int(query[1])], lists[int(query[2])])
``` | instruction | 0 | 14,142 | 5 | 28,284 |
No | output | 1 | 14,142 | 5 | 28,285 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
# coding=utf-8
if __name__ == '__main__':
N, Q = map(int, input().split())
Que = [[] for i in range(N)]
for j in range(Q):
query = list(map(int, input().split()))
if query[0] == 0:
Que[query[1]].append(query[2])
elif query[0] == 1:
print(' '.join(map(str, Que[query[1]])))
elif query[0] == 2:
Que[query[2]].extend(Que[query[1]])
Que[query[1]].clear()
``` | instruction | 0 | 14,143 | 5 | 28,286 |
No | output | 1 | 14,143 | 5 | 28,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
n, q = list(map(int, input().split(' ')))
splice = [[] for i in range(n)]
for i in range(q):
op = list(map(int, input().split(' ')))
if op[0] == 0:
splice[op[1]].append(op[2])
elif op[0] == 1:
print(' '.join(list(map(str, splice[op[1]]))))
elif op[0] == 2:
splice[op[2]].extend(splice[op[1]])
splice[op[1]] = []
``` | instruction | 0 | 14,144 | 5 | 28,288 |
No | output | 1 | 14,144 | 5 | 28,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ lists $L_i$ $(i = 0, 1, ..., n-1)$, perform a sequence of the following operations.
* insert($t$, $x$): Insert an integer $x$ at the end of $L_t$.
* dump($t$): Print all elements in $L_t$.
* splice($s$, $t$): Transfer elements of $L_s$ to the end of $L_t$. $L_s$ becomes empty.
In the initial state, $L_i$ $(i = 0, 1, ..., n-1)$ are empty.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* For a splice operation, $s \ne t$
* For a splice operation, $L_s$ is not empty
* The total number of elements printed by dump operations do not exceed 1,000,000
* $-1,000,000,000 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$n \; q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $s$ $t$
where the first digits 0, 1 and 2 represent insert, dump and splice operations respectively.
Output
For each dump operation, print elements of the corresponding list in a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the list is empty, an empty line should be printed.
Example
Input
3 10
0 0 1
0 0 2
0 0 3
0 1 4
0 1 5
2 1 0
0 2 6
1 0
1 1
1 2
Output
1 2 3 4 5
6
Submitted Solution:
```
def lsprint(lists):
if lists:
print(lists.pop(0), end = '')
for i in lists:
print(' %s' %i, end = '')
print()
print()
else:
pass
def splice(s, t):
return s + t, []
if __name__ == '__main__':
n, q = input().split()
n, q = int(n), int(q)
lists = [[] for _ in range(n)]
for i in range(q):
query = input().split()
if query[0] == "0":
lists[int(query[1])].insert(-1, query[2])
elif query[0] == "1":
lsprint(lists[int(query[1])])
else:
lists[int(query[1])], lists[int(query[2])] = splice(lists[int(query[1])], lists[int(query[2])])
``` | instruction | 0 | 14,145 | 5 | 28,290 |
No | output | 1 | 14,145 | 5 | 28,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
There is an unknown integer x (1≤ x≤ n). You want to find x.
At first, you have a set of integers \{1, 2, …, n\}. You can perform the following operations no more than 10000 times:
* A a: find how many numbers are multiples of a in the current set.
* B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1.
* C a: it means that you know that x=a. This operation can be only performed once.
Remember that in the operation of type B a>1 must hold.
Write a program, that will find the value of x.
Input
The first line contains one integer n (1≤ n≤ 10^5). The remaining parts of the input will be given throughout the interaction process.
Interaction
In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1≤ a≤ n for operations A and C, 2≤ a≤ n for operation B). This line desribes operation you make.
If your operation has type C your program should terminate immediately.
Else your program should read one line containing a single integer, which is the answer to your operation.
After outputting each line, don't forget to flush the output. To do it use:
* fflush(stdout) in C/C++;
* System.out.flush() in Java;
* sys.stdout.flush() in Python;
* flush(output) in Pascal;
* See the documentation for other languages.
It is guaranteed, that the number x is fixed and won't change during the interaction process.
Hacks:
To make a hack, use such input format:
The only line should contain two integers n, x (1 ≤ x ≤ n ≤ 10^5).
Example
Input
10
2
4
0
Output
B 4
A 2
A 8
C 4
Note
Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.
In the first test n=10 and x=4.
Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.
In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.
In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.
In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.
In the fourth operation, you know that x=4, which is the right answer.
Submitted Solution:
```
import sys
n = int(input())
q = 0
if n > 5:
for i in range(2, n // 2):
print('B', i)
sys.stdout.flush()
ans1 = int(input())
print('A', i)
sys.stdout.flush()
ans2 = int(input())
if ans2 == 1:
p = i
q = 1
break
if q == 0:
print('C', 1)
else:
j = 2
myans = p
while p * j <= n:
print('A', p * j)
sys.stdout.flush()
ans = int(input())
if ans == 1:
myans = p * j
j += 1
print('C', myans)
else:
for i in range(2, n + 1):
print('B', i)
sys.stdout.flush()
ans1 = int(input())
print('A', i)
sys.stdout.flush()
ans2 = int(input())
if ans2 == 1:
p = i
q = 1
break
if q == 0:
print('C', 1)
else:
j = 2
myans = p
while p * j <= n:
print('A', p * j)
sys.stdout.flush()
ans = int(input())
if ans == 1:
myans = p * j
j += 1
print('C', myans)
``` | instruction | 0 | 14,361 | 5 | 28,722 |
No | output | 1 | 14,361 | 5 | 28,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
There is an unknown integer x (1≤ x≤ n). You want to find x.
At first, you have a set of integers \{1, 2, …, n\}. You can perform the following operations no more than 10000 times:
* A a: find how many numbers are multiples of a in the current set.
* B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1.
* C a: it means that you know that x=a. This operation can be only performed once.
Remember that in the operation of type B a>1 must hold.
Write a program, that will find the value of x.
Input
The first line contains one integer n (1≤ n≤ 10^5). The remaining parts of the input will be given throughout the interaction process.
Interaction
In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1≤ a≤ n for operations A and C, 2≤ a≤ n for operation B). This line desribes operation you make.
If your operation has type C your program should terminate immediately.
Else your program should read one line containing a single integer, which is the answer to your operation.
After outputting each line, don't forget to flush the output. To do it use:
* fflush(stdout) in C/C++;
* System.out.flush() in Java;
* sys.stdout.flush() in Python;
* flush(output) in Pascal;
* See the documentation for other languages.
It is guaranteed, that the number x is fixed and won't change during the interaction process.
Hacks:
To make a hack, use such input format:
The only line should contain two integers n, x (1 ≤ x ≤ n ≤ 10^5).
Example
Input
10
2
4
0
Output
B 4
A 2
A 8
C 4
Note
Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.
In the first test n=10 and x=4.
Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.
In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.
In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.
In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.
In the fourth operation, you know that x=4, which is the right answer.
Submitted Solution:
```
import sys
N = int(input())
sieve = [-1] * (N + 1)
sieve[0] = sieve[1] = 0
for i in range(N + 1):
if sieve[i] != -1:
continue
else:
index = i * i
while True:
if index > N:
break
sieve[index] = i
index += i
Primes = []
for i in range(N + 1):
if sieve[i] == -1:
Primes.append(i)
CheckConst = 100
currentCheck = 0 # when I have to check
lastCheck = 0 # number of primes checked
isDeleted = [False] * N
deleteCount = 0
maxNumber = N
currentNumber = 1
onePrimeFactor = 0
for indexOut in range(len(Primes)):
elem = Primes[indexOut]
if maxNumber < elem:
break
print("B " + str(elem))
sys.stdout.flush()
curDeleteCount = 0
for i in range(elem - 1,N,elem):
if not isDeleted[i]:
isDeleted[i] = True
curDeleteCount += 1
cnt = int(input())
if cnt != curDeleteCount:
onePrimeFactor = elem
break
currentCheck += 1
deleteCount += curDeleteCount
if currentCheck > CheckConst or indexOut == len(Primes) - 1:
print("A 1")
sys.stdout.flush()
cntNonDeleted = int(input())
if cntNonDeleted + deleteCount != N:
onePrimeFactor = -1
break
lastCheck = indexOut + 1
if onePrimeFactor == 0:
print("C " + str(currentNumber))
else:
for index in range(lastCheck, len(Primes)):
prime = Primes[index]
if prime > maxNumber:
break
print("B " + str(prime))
elem = prime
sys.stdout.flush()
cnt = int(input())
curAliveCount = 0
for i in range(elem - 1,N,elem):
if not isDeleted[i]:
isDeleted[i] = True
curAliveCount += 1
if cnt != curAliveCount:
maxIndex = 1
for i in range(2,100):
if prime ** i > maxNumber:
break
print("A " + str(prime ** i))
sys.stdout.flush()
if(int(input()) != 0):
maxIndex += 1
else:
break
currentNumber *= prime ** maxIndex
maxNumber //= prime ** maxIndex
print("C " + str(currentNumber))
``` | instruction | 0 | 14,362 | 5 | 28,724 |
No | output | 1 | 14,362 | 5 | 28,725 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
There is an unknown integer x (1≤ x≤ n). You want to find x.
At first, you have a set of integers \{1, 2, …, n\}. You can perform the following operations no more than 10000 times:
* A a: find how many numbers are multiples of a in the current set.
* B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1.
* C a: it means that you know that x=a. This operation can be only performed once.
Remember that in the operation of type B a>1 must hold.
Write a program, that will find the value of x.
Input
The first line contains one integer n (1≤ n≤ 10^5). The remaining parts of the input will be given throughout the interaction process.
Interaction
In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1≤ a≤ n for operations A and C, 2≤ a≤ n for operation B). This line desribes operation you make.
If your operation has type C your program should terminate immediately.
Else your program should read one line containing a single integer, which is the answer to your operation.
After outputting each line, don't forget to flush the output. To do it use:
* fflush(stdout) in C/C++;
* System.out.flush() in Java;
* sys.stdout.flush() in Python;
* flush(output) in Pascal;
* See the documentation for other languages.
It is guaranteed, that the number x is fixed and won't change during the interaction process.
Hacks:
To make a hack, use such input format:
The only line should contain two integers n, x (1 ≤ x ≤ n ≤ 10^5).
Example
Input
10
2
4
0
Output
B 4
A 2
A 8
C 4
Note
Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.
In the first test n=10 and x=4.
Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.
In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.
In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.
In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.
In the fourth operation, you know that x=4, which is the right answer.
Submitted Solution:
```
from math import sqrt
MAX_SIZE = 10**5+1
isprime = [True] * MAX_SIZE
p = []
SPF = [None] * (MAX_SIZE)
def manipulated_seive(N):
isprime[0] = isprime[1] = False
for i in range(2, N):
if isprime[i] == True:
p.append(i)
SPF[i] = i
j = 0
while (j < len(p) and
i * p[j] < N and
p[j] <= SPF[i]):
isprime[i * p[j]] = False
SPF[i * p[j]] = p[j]
j += 1
def ask(b,x):
print("{} {}".format(b,x))
n = int(input())
manipulated_seive(10**5+1)
num = 0
ind = 0
while(p[ind]<316):
if (p[ind] > n):
break
ask("B",p[ind])
k = int(input())
ind+=1
num+=1
x = 1
i = 0
ask("A",1)
last_k = int(input())
if(last_k==len(p)-num+1):
m = p.index(317)
i = 0
while(m+i<len(p) and p[m+i]<n):
ask("B",p[m+i])
k = int(input())
i+=1
if(i==100):
ask("A", 1)
k = int(input())
if (last_k != k):
for j in range(100):
ask("B", p[m + j])
k = int(input())
if (k == 1):
x = p[m + j]
ask("C", x)
exit(0)
last_k = k
m += 100
i = 0
ask("A", 1)
k = int(input())
if (last_k != k):
for j in range(i):
ask("B", p[m + j])
k = int(input())
if (k == 1):
x = p[m + j]
ask("C", x)
exit(0)
ask("C",1)
exit(0)
while(p[i]<317):
if(p[i]>n):
break
ask("A",p[i])
k = int(input())
if(k==0):
i+=1
continue
pow = 2
while(k!=0 and p[i]<316):
if(p[i]**pow>n):
pow -= 1
break
ask("A",p[i]**pow)
k = int(input())
if(k==0):
pow -=1
break
pow+=1
x *= p[i]**(pow)
i+=1
m = p.index(317)
i = 0
while(m+i<len(p) and p[m+i]<n):
ask("B",p[m+i])
k = int(input())
i+=1
if(i==100):
ask("A", 1)
k = int(input())
if (last_k != k):
for j in range(100):
ask("B", p[m + j])
k = int(input())
if (k == 1):
x *= p[m + j]
ask("C", x)
exit(0)
last_k = k
m += 100
i = 0
ask("A", 1)
k = int(input())
if (last_k != k):
for j in range(i):
ask("B", p[m + j])
k = int(input())
if (k == 1):
x *= p[m + j]
ask("C", x)
exit(0)
ask("C",x)
``` | instruction | 0 | 14,363 | 5 | 28,726 |
No | output | 1 | 14,363 | 5 | 28,727 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
There is an unknown integer x (1≤ x≤ n). You want to find x.
At first, you have a set of integers \{1, 2, …, n\}. You can perform the following operations no more than 10000 times:
* A a: find how many numbers are multiples of a in the current set.
* B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1.
* C a: it means that you know that x=a. This operation can be only performed once.
Remember that in the operation of type B a>1 must hold.
Write a program, that will find the value of x.
Input
The first line contains one integer n (1≤ n≤ 10^5). The remaining parts of the input will be given throughout the interaction process.
Interaction
In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1≤ a≤ n for operations A and C, 2≤ a≤ n for operation B). This line desribes operation you make.
If your operation has type C your program should terminate immediately.
Else your program should read one line containing a single integer, which is the answer to your operation.
After outputting each line, don't forget to flush the output. To do it use:
* fflush(stdout) in C/C++;
* System.out.flush() in Java;
* sys.stdout.flush() in Python;
* flush(output) in Pascal;
* See the documentation for other languages.
It is guaranteed, that the number x is fixed and won't change during the interaction process.
Hacks:
To make a hack, use such input format:
The only line should contain two integers n, x (1 ≤ x ≤ n ≤ 10^5).
Example
Input
10
2
4
0
Output
B 4
A 2
A 8
C 4
Note
Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.
In the first test n=10 and x=4.
Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.
In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.
In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.
In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.
In the fourth operation, you know that x=4, which is the right answer.
Submitted Solution:
```
MAX_SIZE = 10**5+1
isprime = [True] * MAX_SIZE
p = []
SPF = [None] * (MAX_SIZE)
def manipulated_seive(N):
isprime[0] = isprime[1] = False
for i in range(2, N):
if isprime[i] == True:
p.append(i)
SPF[i] = i
j = 0
while (j < len(p) and
i * p[j] < N and
p[j] <= SPF[i]):
isprime[i * p[j]] = False
SPF[i * p[j]] = p[j]
j += 1
def ask(b,x):
print("{} {}".format(b,x))
n = int(input())
manipulated_seive(10**5+1)
num = 0
ind = 0
while(p[ind]<316):
if (p[ind] > n):
break
ask("B",p[ind])
k = int(input())
ind+=1
num+=1
x = 1
i = 0
ask("A",1)
last_k = int(input())
if(last_k==len(p)-num+1):
m = p.index(317)
i = 0
while(m+i<len(p) and p[m+i]<n):
ask("B",p[m+i])
k = int(input())
i+=1
if(i==100):
ask("A", 1)
k = int(input())
if (last_k-99 == k):
for j in range(100):
ask("A", p[m + j])
k = int(input())
if (k == 1):
x = p[m + j]
ask("C", x)
exit(0)
last_k = k
m += 100
i = 0
ask("A", 1)
k = int(input())
if (last_k-i+1== k):
for j in range(i):
ask("B", p[m + j])
k = int(input())
if (k == 1):
x = p[m + j]
ask("C", x)
exit(0)
ask("C",1)
exit(0)
while(p[i]<317):
if(p[i]>n):
break
ask("A",p[i])
k = int(input())
if(k==0):
i+=1
continue
pow = 2
while(k!=0 and p[i]<316):
if(p[i]**pow>n):
pow -= 1
break
ask("A",p[i]**pow)
k = int(input())
if(k==0):
pow -=1
break
pow+=1
x *= p[i]**(pow)
i+=1
m = p.index(317)
i = 0
if(x>315):
ask("C",x)
exit(0)
while(m+i<len(p) and p[m+i]<n):
ask("B",p[m+i])
k = int(input())
i+=1
if(i==100):
ask("A", 1)
k = int(input())
if (last_k-100 == k):
for j in range(100):
ask("A", p[m + j])
k = int(input())
if (k == 1):
x *= p[m + j]
ask("C", x)
exit(0)
last_k = k
m += 100
i = 0
ask("A",1)
k = int(input())
if(last_k-i==k):
for j in range(i):
ask("A", p[m + j])
k = int(input())
if (k == 1):
x *= p[m + j]
ask("C", x)
exit(0)
ask("C",x)
``` | instruction | 0 | 14,364 | 5 | 28,728 |
No | output | 1 | 14,364 | 5 | 28,729 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
import math as m
x= float(input())
for a in range (1,10+1):
for h in range (1,10+1):
if abs(x - ( (a*h)/ (2* m.sqrt(a*a/4 +h*h) )) ) <= 10**-5:
print (a,h)
quit()
``` | instruction | 0 | 14,568 | 5 | 29,136 |
Yes | output | 1 | 14,568 | 5 | 29,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
import math
s=input()
r=float(s)
def okrugl(fl):
return (round(fl*1000000)/1000000)
flag=1
for a in range(1,11):
for h in range(1,11):
#print(((a*h)/(math.sqrt(a*a+h*h*4))))0
if okrugl((a*h)/(math.sqrt(a*a+h*h*4)))==r:
if flag:
print(a," ",h)
flag=0
``` | instruction | 0 | 14,569 | 5 | 29,138 |
Yes | output | 1 | 14,569 | 5 | 29,139 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
k = float(input())
eps = 10 ** -5
for x in range(1, 11):
for y in range(1, 11):
if abs(x**2 * y**2 / (x**2 + 4 * y**2) - k**2) < eps:
print(x, y)
break
else: continue
break
``` | instruction | 0 | 14,570 | 5 | 29,140 |
Yes | output | 1 | 14,570 | 5 | 29,141 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
from math import sqrt
d = 1e-5
r = float(input())
for a in range(1, 11):
for h in range(1, 11):
if abs((h * a / 2) / sqrt((h ** 2) + ((a / 2) ** 2)) - r) <= d:
ans_a = a
ans_h = h
print(ans_a, ans_h)
``` | instruction | 0 | 14,571 | 5 | 29,142 |
Yes | output | 1 | 14,571 | 5 | 29,143 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
from math import sqrt
import sys
x = float(input())
for a in range(1, 11):
for h in range(1, 11):
if x -( a * h / sqrt(a * a + 4 * h * h)) < 0.000001:
print(a, h)
sys.exit()
``` | instruction | 0 | 14,572 | 5 | 29,144 |
No | output | 1 | 14,572 | 5 | 29,145 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
from math import sqrt
eps = 1e-6
x = float(input())
for a in range(1, 11):
for h in range(1, 11):
if abs(x * sqrt(4 * h * h + a * a) - a * h) < eps:
print(a, h)
break
``` | instruction | 0 | 14,573 | 5 | 29,146 |
No | output | 1 | 14,573 | 5 | 29,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
print (10, 10)
``` | instruction | 0 | 14,574 | 5 | 29,148 |
No | output | 1 | 14,574 | 5 | 29,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).
Output
Output two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.
Examples
Input
1.200000
Output
3 2
Input
2.572479
Output
10 3
Input
4.024922
Output
9 9
Submitted Solution:
```
print(10, 1)
``` | instruction | 0 | 14,575 | 5 | 29,150 |
No | output | 1 | 14,575 | 5 | 29,151 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144 | instruction | 0 | 14,758 | 5 | 29,516 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
# sys.setrecursionlimit(10**6)
# readline = sys.stdin.buffer.readline
readline = sys.stdin.readline
INF = 1 << 50
def read_int():
return int(readline())
def read_int_n():
return list(map(int, readline().split()))
def read_float():
return float(readline())
def read_float_n():
return list(map(float, readline().split()))
def read_str():
return readline().strip()
def read_str_n():
return readline().strip().split()
def ep(*args):
print(*args, file=sys.stderr)
def mt(f):
import time
def wrap(*args, **kwargs):
s = time.perf_counter()
ret = f(*args, **kwargs)
e = time.perf_counter()
ep(e - s, 'sec')
return ret
return wrap
def divisor(n):
for i in range(1, int(n**0.5)+1):
if n % i == 0:
yield i
if i != n // i:
yield n // i
def exEuclid(a, mod):
b = mod
s, u = 1, 0
while b:
q = a // b
a, b = b, a % b
s, u = u, s - q * u
return a, s % mod
def crt(R, M):
assert len(R) == len(M)
N = len(R)
r0, m0 = 0, 1
for r, m in zip(R, M):
assert m >= 1
r %= m
if m0 < m:
r0, r = r, r0
m0, m = m, m0
if m0 % m == 0:
if r0 % m != r:
return (0, 0)
continue
g, im = exEuclid(m0, m)
u = m // g
if (r - r0) % g:
return (0, 0)
x = (r - r0) // g % u * im % u
r0 += x * m0
m0 *= u
if r0 < 0:
r0 += m0
return (r0, m0)
@mt
def slv(N):
def f(n):
return (n+1)*n // 2
cand = list(divisor(2*N))
cand.sort()
ans = INF
for x in cand:
kc, _ = crt([0, -1], (x, 2*N//x))
if kc != 0:
ans = min(ans, kc)
return ans
def main():
N = read_int()
print(slv(N))
if __name__ == '__main__':
main()
``` | output | 1 | 14,758 | 5 | 29,517 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144 | instruction | 0 | 14,761 | 5 | 29,522 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
n = int(input()) * 2
D = []
for i in range(2, int(n**0.5) + 1):
d = 1
while n%i == 0:
n //= i
d *= i
if d != 1:
D.append(d)
if n == 1:
break
if n != 1:
D.append(n)
# print(D)
# 拡張Euclidの互除法。ap + bq = gcd(a, b) となる p, q, d=gcd(a, b) を返す。
def extgcd(a, b):
if b == 0:
return 1, 0, a
q, p, d = extgcd(b, a%b)
q -= (a // b) * p
return p, q, d
def crt(R, M): # 中国剰余定理。Rは余り、Mは割る数の配列。不定なら(0,1)、不能なら(0,0)が返る。
r = 0
m = 1
for i in range(len(R)):
p, _, d = extgcd(m, M[i])
if (R[i] - r) % d != 0:
return (0, 0)
tmp = (R[i] - r) // d * p % (M[i] // d)
r += m * tmp
m *= M[i] // d
return (r % m, m)
ans = float("inf")
# Rs = []
for i in range(1, 2**len(D)):
ib = format(i, "b").zfill(len(D))
R = [0] * len(D)
for j in range(len(D)):
if ib[j] == "1":
R[j] = D[j]-1
ans = min(ans, crt(R, D)[0])
print(ans)
``` | output | 1 | 14,761 | 5 | 29,523 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144 | instruction | 0 | 14,762 | 5 | 29,524 |
"Correct Solution:
```
from itertools import product
def main():
n = int(input())
n_copy = n
if n == 1:
print(1)
exit()
if n % 2 == 0:
ans = 2 * n - 1
n *= 2
else:
ans = n - 1
factors = []
for p in range(2, n):
if p * p > n:
if n > 1:
factors.append(n)
break
if n % p == 0:
cnt = 0
while n % p == 0:
cnt += 1
n //= p
factors.append(p ** cnt)
for tf in product([True, False], repeat=len(factors)):
a, b = 1, 1
for i in range(len(factors)):
if tf[i]:
a *= factors[i]
else:
b *= factors[i]
if a == 1 or b == 1:
continue
if a < b:
a, b = b, a
# Euclidean Algorithm
# a*x - b*y = 1
# quotient: 商
l = []
quo = []
while a % b > 1:
l.append(a)
a = b
quo.append(0)
quo[-1], b = divmod(l[-1], b)
x, y = 1, a//b
flag = True
while l:
if flag:
x += y * quo.pop()
b = l.pop()
else:
y += x * quo.pop()
a = l.pop()
flag = not flag
if ans > b * y:
ans = b * y
print(ans)
main()
``` | output | 1 | 14,762 | 5 | 29,525 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144 | instruction | 0 | 14,763 | 5 | 29,526 |
"Correct Solution:
```
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")
n = int(input())
def factor(n, m=None):
# mを与えると、高々その素因数まで見て、残りは分解せずにそのまま出力する
arr = {}
temp = n
M = int(-(-n**0.5//1))+1
if m is not None:
M = min(m+1, M)
for i in range(2, M):
if i>temp:
break
if temp%i==0:
cnt=0
while temp%i==0:
cnt+=1
temp //= i
arr[i] = cnt
if temp!=1:
arr[temp] = 1
if not arr:
arr[n] = 1
return arr
n *= 2
f = factor(n)
# print(f)
from itertools import product
ans = n-1
def gcd2(a, b):
"""a*x + b*y = gcd(a,b)なるx,yも求める
"""
l = []
while b:
l.append(divmod(a,b))
a, b = b, a%b
x, y = 1, 0
for aa,bb in l[::-1]:
x, y = y, x - aa*y
return a, x, y
def sub(x,y):
g,k,l = gcd2(x, -y)
if g!=1:
return None
return abs(k*x)
for ks in product(*[range(2) for _ in f.values()]):
val = 1
val2 = 1
for k,v in zip(ks, f.keys()):
if k:
val *= pow(v,f[v])
else:
val2 *= pow(v,f[v])
# print(val*val2)
if val==1 or val2==1:
continue
res = gcd2(val, -val2)
if res is not None and abs(res[0])==1:
# print(val,val2,res)
ans = min(ans, abs(val*res[1]))
print(ans)
``` | output | 1 | 14,763 | 5 | 29,527 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144 | instruction | 0 | 14,765 | 5 | 29,530 |
"Correct Solution:
```
def euclid(x, y):
c0, c1 = x, y
a0, a1 = 1, 0
b0, b1 = 0, 1
while c1 != 0:
m = c0 % c1
q = c0 // c1
c0, c1 = c1, m
a0, a1 = a1, (a0 - q * a1)
b0, b1 = b1, (b0 - q * b1)
return a0, b0
n=int(input())
n=n*2
soinsu=[]
num=n
for i in range(2,max(20,n)):
if(i*i>n):
if(num!=1):
soinsu.append([num,1])
break
if(num%i!=0):
continue
cnt=0
while(num%i==0):
cnt+=1
num//=i
soinsu.append([i,cnt])
kazu=len(soinsu)
ans=[]
for i in range(2**(kazu-1)):
a=1
for j in range(kazu):
if((i&1<<j)!=0):
a*=soinsu[j][0]**soinsu[j][1]
b=n//a
c,d=euclid(a,b)
if(c*d==0):
c+=b
d+=a
ans.append(max(a*c,b*d))
if(kazu==1):
print(min(ans)-2)
else:
print(min(ans)-1)
``` | output | 1 | 14,765 | 5 | 29,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144
Submitted Solution:
```
#素因数分解、計算量はO(√N)
from collections import defaultdict
def factorize(n):
b = 2
dic = defaultdict(lambda: 0)
while b * b <= n:
while n % b == 0:
n //= b
dic[b] += 1
b = b + 1
if n > 1:
dic[n] += 1
return dic
N = int(input())
fct = factorize(2*N)
lis = []
for k,v in fct.items():
lis.append(pow(k,v))
ans = 10**18
from itertools import groupby, accumulate, product, permutations, combinations
for pro in product([1,0],repeat=len(lis)):
prod1 = 1
for i,p in enumerate(pro):
if p==1:
prod1 *= lis[i]
prod2 = (N*2)//prod1
if prod1<prod2:
# prod1,prod2 = prod2,prod1
continue
for i in range(1,prod2+1):
if prod1*i>ans:
break
if (prod1*i-1)%prod2==0:
ans = min(ans, prod1*i-1)
break
if (prod1*i+1)%prod2==0:
ans = min(ans, prod1*i)
break
print(ans)
``` | instruction | 0 | 14,766 | 5 | 29,532 |
Yes | output | 1 | 14,766 | 5 | 29,533 |
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