message stringlengths 2 57.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91 | instruction | 0 | 6,732 | 22 | 13,464 |
Tags: math, number theory
Correct Solution:
```
import sys
from math import gcd
input=sys.stdin.readline
t=int(input())
for ii in range(t):
a,b,q=map(int,input().split())
c=a*b//gcd(a,b)
f=0
d=[0]
for i in range(c):
if (i%a)%b!=(i%b)%a:
f+=1
d.append(f)
ans=[]
for i in range(q):
l,r=map(int,input().split())
nl=l-l%c
nr=r+(c-r%c)-1
p=(nr-nl+1)//c
ff=0
tmp=p*f
tmp-=(d[(l%c)]+d[-1]-d[r%c+1])
ans.append(tmp)
print(*ans)
``` | output | 1 | 6,732 | 22 | 13,465 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91 | instruction | 0 | 6,733 | 22 | 13,466 |
Tags: math, number theory
Correct Solution:
```
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import sys
input = sys.stdin.readline
M = mod = 10**9 + 7
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
def li():return [int(i) for i in input().split()]
def st():return input()
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]
def giveab(a,b):
l = []
for i in range(1,a * b + 1,1):
l.append(1 if ((i%a)%b) != ((i%b)%a) else 0)
return l[:]
def giveforanum(r,s,l):
temp = r//(a * b)
up = temp*s
r %= (a * b)
return up + l[r]
for _ in range(val()):
a,b,q = li()
l1 = giveab(a,b)
pref = [0]
for i in l1:pref.append(pref[-1] + i)
s = sum(l1)
for i in range(q):
l,r = li()
print(giveforanum(r,s,pref) - giveforanum(l-1,s,pref))
``` | output | 1 | 6,733 | 22 | 13,467 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91 | instruction | 0 | 6,734 | 22 | 13,468 |
Tags: math, number theory
Correct Solution:
```
import sys
#
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
#
# range=xrange
from math import gcd
def go():
# n = int(input())
a,b,q = map(int, input().split())
# a, b = map(int, input().split())
g=a*b//gcd(a,b)
m=max(a,b)
def until(v):
result = ((v+1)//g)*m + min((v+1)%g,m)
result = v+1-result
# print ('-',v,result)
return result
res = []
for _ in range(q):
l, r = map(int, input().split())
res.append(until(r)-until(l-1))
return ' '.join(map(str,res))
# x,s = map(int,input().split())
t = int(input())
# t = 1
ans = []
for _ in range(t):
# print(go())
ans.append(str(go()))
#
print('\n'.join(ans))
``` | output | 1 | 6,734 | 22 | 13,469 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91 | instruction | 0 | 6,735 | 22 | 13,470 |
Tags: math, number theory
Correct Solution:
```
import math
def check(arr, a, b):
d = []
ll = a*b//math.gcd(a, b)
for i in range(1, ll+1):
if i%a%b != i%b%a:
d.append(1)
else:
d.append(0)
for i in range(1, len(d)):
if d[i] == 1:
d[i] = d[i-1] + 1
else:
d[i] = d[i-1]
result = []
last = d[-1]
for l, r in arr:
p = 1
q = 1
kk = last*((r//ll) - (l-1)//ll)
l -= 1
r = r % ll
if r == 0:
p = 0
else:
r -= 1
l = l % ll
if l == 0:
q = 0
else:
l -= 1
result.append(p*d[r] - q*d[l] + kk)
return result
t = int(input())
while t:
a, b, q = list(map(int, input().split()))
arr = []
for i in range(q):
arr.append(list(map(int, input().split())))
result = check(arr, a, b)
for i in result:
print(i, end=" " )
print()
t-= 1
``` | output | 1 | 6,735 | 22 | 13,471 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91 | instruction | 0 | 6,736 | 22 | 13,472 |
Tags: math, number theory
Correct Solution:
```
'''
Auther: ghoshashis545 Ashis Ghosh
College: jalpaiguri Govt Enggineerin College
Date:26/04/2020
'''
from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
from itertools import permutations
from datetime import datetime
from math import ceil,sqrt,log,gcd
def ii():return int(input())
def si():return input()
def mi():return map(int,input().split())
def li():return list(mi())
abc='abcdefghijklmnopqrstuvwxyz'
abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
mod=1000000007
#mod=998244353
inf = float("inf")
vow=['a','e','i','o','u']
dx,dy=[-1,1,0,0],[0,0,1,-1]
def powmod(a,b):
a%=mod
if(a==0):
return 0
res=1
while(b>0):
if(b&1):
res=(res*a)%mod
a=(a*a)%mod
b>>=1
return res
def func(x,y,c):
c1=x//y
ans=(c1*c)
x%=y
x+=1
if(x<c):
ans+=(x-c)
# print(ans)
return ans
def main():
for _ in range(ii()):
a,b,q=mi()
if(b>a):
a,b=b,a
x=a
y=(a*b)//gcd(a,b)
for i in range(q):
l,r=mi()
l-=1
if(a==b or r<a):
print('0',end=" ")
continue
if(r>=y):
ans=r-func(r,y,x)-a+1
else:
ans=(r-a+1)
if(l>=y):
ans1=l-func(l,y,x)-a+1
else:
if(l<a):
ans1=0
else:
ans1=(l-a+1)
# print(ans,ans1)
print(ans-ans1,end=" ")
print()
if __name__ == "__main__":
main()
``` | output | 1 | 6,736 | 22 | 13,473 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91 | instruction | 0 | 6,737 | 22 | 13,474 |
Tags: math, number theory
Correct Solution:
```
from math import gcd
finaans=[]
for t in range(int(input())):
a,b,q=[int(x) for x in input().split()]
l=(a*b)//gcd(a,b)
ans=[]
for k in range(q):
q1,q2=[int(x) for x in input().split()]
p=(q1-1)//l
q=q2//l
s1=q2-(q*max(a,b)+min(max(a,b),(q2%l)+1))
s2=q1-1-(p*max(a,b)+min(max(a,b),((q1-1)%l)+1))
ans.append(s1-s2)
finaans.append(ans)
for it in finaans:
print(*it)
``` | output | 1 | 6,737 | 22 | 13,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
def gcd(a,b):
if b==0:
return a
else:
return gcd(b,a%b)
def lcm(a,b):
return a*(b//gcd(a,b))
for _ in range(int(input())):
a,b,s=list(map(int,input().split()))
p=lcm(a,b)
q=max(a,b)
lis=[]
for _ in range(s):
l,r=map(int,input().split())
a1=l//p
a2=r//p
b1=l%p
b2=r%p
ans=0
if a1==a2:
if b1<q:
if b2<q:
ans+=b2-b1+1
else:
ans+=q-b1
else:
ans+=(a2-a1-1)*q
if b1<q:
ans+=q-b1
if b2>=q:
ans+=q
if b2<q:
ans+=b2+1
lis.append(r-l+1-ans)
print(*lis)
``` | instruction | 0 | 6,738 | 22 | 13,476 |
Yes | output | 1 | 6,738 | 22 | 13,477 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
import math
def not_equal(a, b, i):
if i <= b-1:
return 0
# Get the lcm of a and b
l = a*b // math.gcd(a, b)
# The numbers up to the minimum always satisfy the condition
out = i - b + 1
# Subtract the terms k*l + c, k \in N, c < b
n_seqs = (i - b) // l
out -= n_seqs * b
# Add the terms that you may have missed when the modulus is close
mod = i % l
if mod < b:
out -= (mod+1)
return out
def naive_not_equal(a, b, val):
count = 0
for i in range(val+1):
if (i % a) % b != (i % b) % a:
count += 1
return count
t = int(input())
for _ in range(t):
a, b, q = map(int, input().split())
# Put a and b in order (a < b)
if a > b:
a, b = b, a
out = []
for _ in range(q):
l, r = map(int, input().split())
lhs = not_equal(a, b, l-1)
rhs = not_equal(a, b, r)
ans = rhs - lhs
out.append(str(ans))
print(' '.join(out))
``` | instruction | 0 | 6,739 | 22 | 13,478 |
Yes | output | 1 | 6,739 | 22 | 13,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
import math
import os,io
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def findv(lcm,l,r,b):
p = max(min(r,b),l)
s = r-p+1
x1 = p//lcm
x2 = r//lcm
if x1*lcm+b > p:
s -= b-p%lcm
x1 += 1
if x2*lcm+b <= r:
s -= b*(x2-x1+1)
else:
s -= b*(x2-x1)+ r%lcm + 1
return s
cases = int(input())
for t in range(cases):
a,b,q = list(map(int,input().split()))
a,b = min(a,b),max(a,b)
lcm = (a*b)//math.gcd(a,b)
out = []
for i in range(q):
l,r = list(map(int,input().split()))
if b>r:
out.append(0)
else:
out.append(findv(lcm, l, r, b))
print(*out)
``` | instruction | 0 | 6,740 | 22 | 13,480 |
Yes | output | 1 | 6,740 | 22 | 13,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
for _ in range(int(input())):
a,b,q = map(int,input().split())
p = [0]*(a*b)
for j in range(1,a*b):
p[j] = p[j-1]
if (((j % a) % b) != ((j % b) % a)):
p[j] = p[j] + 1
m = []
for k in range(q):
l,r = map(int,input().split())
x = r//len(p)
y = (l-1)//len(p)
m.append(p[r % (len(p))] - p[(l - 1) % (len(p))] + (x - y) * p[-1])
print(*m)
``` | instruction | 0 | 6,741 | 22 | 13,482 |
Yes | output | 1 | 6,741 | 22 | 13,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
def gcd(a,b):
# Everything divides 0
if (a == 0):
return b
if (b == 0):
return a
# base case
if (a == b):
return a
# a is greater
if (a > b):
return gcd(a-b, b)
return gcd(a, b-a)
T=int(input())
for _ in range(T):
a,b,q=input().split()
a=int(a)
b=int(b)
q=int(q)
answer=[]
lcm_ab=int((a*b)/gcd(a,b))
for _1 in range(q):
x,y=input().split()
x=int(x)
y=int(y)
if x>b:
temp=y-x+1
else:
temp=y-b+1
if temp>0:
count=temp
else:
count=0
count1=0
temp1=int(x/lcm_ab)
if x-temp1*lcm_ab<b and temp1>0:
count1+=temp1*lcm_ab+b-x
temp2=int(y/lcm_ab)
if y-temp2*lcm_ab<b and temp2>0:
count1+=y-temp2*lcm_ab
count1+=b*(temp2-temp1)
answer.append(count-count1)
print(*answer)
``` | instruction | 0 | 6,742 | 22 | 13,484 |
No | output | 1 | 6,742 | 22 | 13,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
def readInts():
return list(map(int, input().split()))
def readInt():
return int(input())
def g(a, b, r):
times = (r + 1) // (a * b)
rem = (r + 1) % (a * b)
res = 0
for x in range(a * b):
if x > r:
break
if (x % a) % b != (x % b) % a:
res += times
if rem > 0:
res += 1
rem -= 1
return res
def f(a, b, l, r):
if a == b:
return 0
# a < b
res1 = g(a, b, r)
res2 = g(a, b, l - 1)
return res1 - res2
def solve(a, b, q):
ans = []
for _ in range(q):
l, r = readInts()
ans.append(f(min(a, b), max(a, b), l, r))
for x in ans:
print(x, end=" ")
print()
def main():
t = readInt()
for i in range(t):
a, b, q = readInts()
solve(a, b, q)
main()
``` | instruction | 0 | 6,743 | 22 | 13,486 |
No | output | 1 | 6,743 | 22 | 13,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
import math
a = 0
b = 0
p = 0
def get(x):
k = int(x / p)
return int(x-(k*max(a, b)-1+min(max(a, b), (x-k*p+1))))
for _ in range(int(input())):
a, b, q = map(int, input().split())
p = math.gcd(a, b)
p = a * b / p
for k in range(q):
l, r = map(int, input().split())
print(get(r) - get(l-1), end=' ')
print(" ")
``` | instruction | 0 | 6,744 | 22 | 13,488 |
No | output | 1 | 6,744 | 22 | 13,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b, and q queries. The i-th query consists of two numbers l_i and r_i, and the answer to it is the number of integers x such that l_i β€ x β€ r_i, and ((x mod a) mod b) β ((x mod b) mod a). Calculate the answer for each query.
Recall that y mod z is the remainder of the division of y by z. For example, 5 mod 3 = 2, 7 mod 8 = 7, 9 mod 4 = 1, 9 mod 9 = 0.
Input
The first line contains one integer t (1 β€ t β€ 100) β the number of test cases. Then the test cases follow.
The first line of each test case contains three integers a, b and q (1 β€ a, b β€ 200; 1 β€ q β€ 500).
Then q lines follow, each containing two integers l_i and r_i (1 β€ l_i β€ r_i β€ 10^{18}) for the corresponding query.
Output
For each test case, print q integers β the answers to the queries of this test case in the order they appear.
Example
Input
2
4 6 5
1 1
1 3
1 5
1 7
1 9
7 10 2
7 8
100 200
Output
0 0 0 2 4
0 91
Submitted Solution:
```
# Contest No.: Edu 86
# Problem No.: C
# Solver: JEMINI
# Date: 20200426
import sys
def gcd(a: int, b: int) -> int:
if a < b:
a, b = b, a
if b == 0:
return a
else:
return gcd(b, a % b)
def main():
t = int(input())
for _ in range(t):
a, b, q = map(int, sys.stdin.readline().split())
flag = None
modVal = None
if a == 1 or b == 1 or a == b:
flag = 0
elif max(a, b) % min(a, b) == 0:
flag = 1
modVal = min(a, b)
else:
flag = 2
modVal = a * b // gcd(a, b)
checkList = [False] * modVal
loopSum = 0
for i in range(modVal):
if ((i % a) % b) != ((i % b) % a):
checkList[i] = True
loopSum += 1
for i in range(q):
x, y = map(int, sys.stdin.readline().split())
if flag == 0:
print(0, end = " ")
elif flag == 1:
ans = y - x + 1
tempL = x + (modVal - x % modVal) % modVal
tempR = y + (modVal - y % modVal)
ans -= tempR // modVal - tempL // modVal
print(ans, end = " ")
else:
ans = sum(checkList[x % modVal:y % modVal + 1]) + (y // modVal - x // modVal) * loopSum
print(ans, end = " ")
print("")
return
if __name__ == "__main__":
main()
``` | instruction | 0 | 6,745 | 22 | 13,490 |
No | output | 1 | 6,745 | 22 | 13,491 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
John Doe offered his sister Jane Doe find the gcd of some set of numbers a.
Gcd is a positive integer g, such that all number from the set are evenly divisible by g and there isn't such g' (g' > g), that all numbers of the set are evenly divisible by g'.
Unfortunately Jane couldn't cope with the task and John offered her to find the ghd of the same subset of numbers.
Ghd is a positive integer g, such that at least half of numbers from the set are evenly divisible by g and there isn't such g' (g' > g) that at least half of the numbers from the set are evenly divisible by g'.
Jane coped with the task for two hours. Please try it, too.
Input
The first line contains an integer n (1 β€ n β€ 106) showing how many numbers are in set a. The second line contains space-separated integers a1, a2, ..., an (1 β€ ai β€ 1012). Please note, that given set can contain equal numbers.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the %I64d specifier.
Output
Print a single integer g β the Ghd of set a.
Examples
Input
6
6 2 3 4 5 6
Output
3
Input
5
5 5 6 10 15
Output
5
Submitted Solution:
```
from random import randrange, seed
from sys import stdin
def read_integers():
return list(map(int, stdin.readline().strip().split()))
def decompose(num, visited):
if num in visited:
return []
factors = []
i = 2
while i * i <= num:
quo, rem = divmod(num, i)
if i not in visited and rem == 0:
factors.append(i)
visited.add(i)
if quo not in visited and quo != i:
factors.append(quo)
visited.add(quo)
i += 1
factors.append(num)
visited.add(num)
factors.sort(reverse=True)
return factors
def ghd(arr):
n_trials = 10
max_f = 1
visited = set()
cache = {}
sample_arr = [arr[randrange(0, len(arr))] for _ in range(700)] if len(arr) >= 10 ** 5 else arr
for i in range(n_trials):
for f in decompose(arr[randrange(0, len(arr))], visited):
if any(f < x and x % f == 0 for x in cache):
cache[f] = -1
visited.add(f)
continue
cnt = sum(x % f == 0 for x in sample_arr)
if cnt * 2 >= len(sample_arr):
max_f = max(max_f, f)
cache[f] = cnt
return max_f
if True:
from time import time
seed(time())
_, = read_integers()
arr = read_integers()
print(ghd(arr))
``` | instruction | 0 | 6,973 | 22 | 13,946 |
No | output | 1 | 6,973 | 22 | 13,947 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
John Doe offered his sister Jane Doe find the gcd of some set of numbers a.
Gcd is a positive integer g, such that all number from the set are evenly divisible by g and there isn't such g' (g' > g), that all numbers of the set are evenly divisible by g'.
Unfortunately Jane couldn't cope with the task and John offered her to find the ghd of the same subset of numbers.
Ghd is a positive integer g, such that at least half of numbers from the set are evenly divisible by g and there isn't such g' (g' > g) that at least half of the numbers from the set are evenly divisible by g'.
Jane coped with the task for two hours. Please try it, too.
Input
The first line contains an integer n (1 β€ n β€ 106) showing how many numbers are in set a. The second line contains space-separated integers a1, a2, ..., an (1 β€ ai β€ 1012). Please note, that given set can contain equal numbers.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the %I64d specifier.
Output
Print a single integer g β the Ghd of set a.
Examples
Input
6
6 2 3 4 5 6
Output
3
Input
5
5 5 6 10 15
Output
5
Submitted Solution:
```
from random import randrange, seed
from sys import stdin
def read_integers():
return list(map(int, stdin.readline().strip().split()))
def decompose(num, visited):
if num in visited:
return []
factors = []
i = 2
while i * i <= num:
quo, rem = divmod(num, i)
if i not in visited and rem == 0:
factors.append(i)
visited.add(i)
if quo not in visited and quo != i:
factors.append(quo)
visited.add(quo)
i += 1
factors.append(num)
visited.add(num)
factors.sort(reverse=True)
return factors
def ghd(arr):
n_trials = 15
max_f = 1
visited = set()
cache = {}
sample_arr = [arr[randrange(0, len(arr))] for _ in range(700)] if len(arr) >= 10 ** 5 else arr
for i in range(n_trials):
for f in decompose(arr[randrange(0, len(arr))], visited):
if any(f < x and x % f == 0 for x in cache):
cache[f] = -1
visited.add(f)
continue
cnt = sum(x % f == 0 for x in sample_arr)
if cnt * 2 >= len(sample_arr):
max_f = max(max_f, f)
cache[f] = cnt
return max_f
if True:
from time import time
seed(time())
_, = read_integers()
arr = read_integers()
print(ghd(arr))
``` | instruction | 0 | 6,974 | 22 | 13,948 |
No | output | 1 | 6,974 | 22 | 13,949 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
John Doe offered his sister Jane Doe find the gcd of some set of numbers a.
Gcd is a positive integer g, such that all number from the set are evenly divisible by g and there isn't such g' (g' > g), that all numbers of the set are evenly divisible by g'.
Unfortunately Jane couldn't cope with the task and John offered her to find the ghd of the same subset of numbers.
Ghd is a positive integer g, such that at least half of numbers from the set are evenly divisible by g and there isn't such g' (g' > g) that at least half of the numbers from the set are evenly divisible by g'.
Jane coped with the task for two hours. Please try it, too.
Input
The first line contains an integer n (1 β€ n β€ 106) showing how many numbers are in set a. The second line contains space-separated integers a1, a2, ..., an (1 β€ ai β€ 1012). Please note, that given set can contain equal numbers.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the %I64d specifier.
Output
Print a single integer g β the Ghd of set a.
Examples
Input
6
6 2 3 4 5 6
Output
3
Input
5
5 5 6 10 15
Output
5
Submitted Solution:
```
from typing import List, Set
from random import randrange
from sys import stdin
from functools import reduce, lru_cache
def read_integers():
return list(map(int, stdin.readline().strip().split()))
@lru_cache(None)
def decompose(num: int) -> List[int]:
if num <= 1:
return []
i = 2
while i ** 2 < num:
if num % i == 0:
left = decompose(i)
right = decompose(num // i)
return left + right
i += 1
return [num]
def ghd(arr: List[int]) -> int:
n_trials = 30
rd_lst = [randrange(0, len(arr)) for _ in range(n_trials)] # type: List[int]
factors = set(reduce(list.__add__, (decompose(arr[rd]) for rd in rd_lst))) # type: Set[int]
cnts = {f: sum(num % f == 0 for num in arr) for f in factors}
cnts = {k: v for k, v in cnts.items() if v * 2 >= len(arr)}
return max(cnts.keys()) if cnts else 1
if True:
_, = read_integers()
input_arr = read_integers()
print(ghd(input_arr))
``` | instruction | 0 | 6,975 | 22 | 13,950 |
No | output | 1 | 6,975 | 22 | 13,951 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
John Doe offered his sister Jane Doe find the gcd of some set of numbers a.
Gcd is a positive integer g, such that all number from the set are evenly divisible by g and there isn't such g' (g' > g), that all numbers of the set are evenly divisible by g'.
Unfortunately Jane couldn't cope with the task and John offered her to find the ghd of the same subset of numbers.
Ghd is a positive integer g, such that at least half of numbers from the set are evenly divisible by g and there isn't such g' (g' > g) that at least half of the numbers from the set are evenly divisible by g'.
Jane coped with the task for two hours. Please try it, too.
Input
The first line contains an integer n (1 β€ n β€ 106) showing how many numbers are in set a. The second line contains space-separated integers a1, a2, ..., an (1 β€ ai β€ 1012). Please note, that given set can contain equal numbers.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the %I64d specifier.
Output
Print a single integer g β the Ghd of set a.
Examples
Input
6
6 2 3 4 5 6
Output
3
Input
5
5 5 6 10 15
Output
5
Submitted Solution:
```
from random import randrange, seed
from sys import stdin
def read_integers():
return list(map(int, stdin.readline().strip().split()))
def decompose(num, visited):
if num in visited:
return []
factors = []
i = 2
while i * i <= num:
quo, rem = divmod(num, i)
if i not in visited and rem == 0:
factors.append(i)
visited.add(i)
if quo not in visited and quo != i:
factors.append(quo)
visited.add(quo)
i += 1
factors.append(num)
visited.add(num)
factors.sort(reverse=True)
return factors
def ghd(arr):
n_trials = 15
max_f = 1
visited = set()
cache = {}
sample_arr = [arr[randrange(0, len(arr))] for _ in range(1000)] if len(arr) >= 10 ** 5 else arr
for i in range(n_trials):
for f in decompose(arr[randrange(0, len(arr))], visited):
if any(f < x and x % f == 0 for x in cache):
cache[f] = -1
visited.add(f)
continue
cnt = sum(x % f == 0 for x in sample_arr)
if cnt * 2 >= len(sample_arr):
max_f = max(max_f, f)
cache[f] = cnt
return max_f
if True:
from time import time
seed(time())
_, = read_integers()
arr = read_integers()
print(ghd(arr))
``` | instruction | 0 | 6,976 | 22 | 13,952 |
No | output | 1 | 6,976 | 22 | 13,953 |
Provide a correct Python 3 solution for this coding contest problem.
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 β€ n β€ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439 | instruction | 0 | 7,436 | 22 | 14,872 |
"Correct Solution:
```
# AOJ 0222 Prime Quadruplet
# Python3 2018.6.23 bal4u
# From Wekipedia (https://en.wikipedia.org/wiki/Prime_quadruplet)
# All prime quadruplets except {5, 7, 11, 13} are of the form
# {30n + 11, 30n + 13, 30n + 17, 30n + 19} for some integer n.
MAX = 899
diff = (0,3,3,21,22,13,7,39,7,73, \
126,119,88,3,11,66,29,17,53,42, \
101,214,104,298,252,133,255,141,76,91, \
168,81,45,56,203,301,43,66,291,223, \
92,97,442,290,437,281,38,144,549,241, \
29,192,11,518,266,490,122,130,13,329, \
85,209,71,241,290,18,301,52,120,34, \
50,805,276,217,182,53,209,155,77,468, \
448,29,90,85,91,7,146,21,309,234, \
60,213,511,59,273,364,57,77,87,231, \
452,168,154,346,273,588,11,91,322,335, \
140,221,87,442,297,95,321,498,146,182, \
8,38,11,679,111,120,83,36,59,462, \
32,349,448,333,644,63,101,960,161,759, \
255,354,270,52,200,133,112,297,298,27, \
74,577,25,182,280,584,756,266,287,277, \
119,31,561,59,179,630,34,98,1,84, \
217,234,4,48,127,528,679,35,108,15, \
752,60,31,228,559,7,35,56,43,10, \
151,374,297,294,14,60,196,133,18,63, \
63,17,35,290,953,584,66,102,427,4, \
357,507,441,420,802,14,66,171,252,88, \
14,364,32,220,66,256,427,651,52,287, \
987,214,161,319,241,1333,190,325,63,500, \
1026,60,13,112,238,144,137,349,417,32, \
164,196,115,735,200,382,273,104,119,214, \
665,235,297,665,25,34,211,280,542,375, \
188,42,134,573,350,106,17,112,676,1095, \
403,62,193,60,13,116,60,255,609,350, \
7,165,661,25,748,176,10,283,144,987, \
389,59,60,342,112,144,31,98,676,297, \
652,189,56,34,441,50,314,266,29,546, \
297,39,657,46,703,70,270,221,122,767, \
13,134,318,1222,84,650,371,92,164,760, \
318,175,158,679,496,389,273,38,676,270, \
902,228,143,196,18,287,102,409,612,1, \
56,269,311,714,1092,176,34,165,143,438, \
266,249,97,442,105,7,913,81,80,871, \
497,585,574,11,220,94,855,132,473,836, \
301,7,833,63,1145,60,1886,382,111,43, \
111,319,431,108,297,60,878,799,133,472, \
529,420,241,46,231,304,616,1145,595,447, \
589,76,399,865,154,101,119,739,528,673, \
49,994,412,1072,6,25,3,49,126,1079, \
1141,66,220,932,1049,561,692,764,476,248, \
200,1897,658,644,24,399,143,1331,839,1, \
1077,760,11,34,658,36,647,21,528,242, \
98,529,24,1117,192,396,930,224,365,66, \
557,377,757,322,203,335,770,155,97,21, \
665,484,553,321,207,116,574,272,287,253, \
637,259,38,263,62,1268,451,693,756,630, \
357,105,32,581,455,153,540,350,91,210, \
409,270,377,442,490,615,424,52,890,199, \
102,1746,462,749,24,644,540,220,840,1656, \
223,74,434,179,665,923,428,307,875,50, \
2387,276,109,363,529,550,139,798,176,150, \
297,123,66,266,414,17,130,1344,300,1799, \
8,1176,279,351,461,396,112,626,498,931, \
2782,123,1253,780,781,1119,46,39,847,468, \
1037,1144,63,332,294,1082,525,459,220,70, \
231,31,1029,256,290,662,242,98,252,13, \
1008,64,346,1211,119,802,189,272,298,122, \
697,319,195,273,410,1221,365,885,322,52, \
847,165,112,67,812,630,801,87,60,424, \
630,867,231,123,308,396,76,119,60,203, \
17,63,553,931,147,588,127,437,164,43, \
14,371,115,150,354,315,473,3,1221,245, \
36,272,214,24,385,249,182,445,171,35, \
921,300,1558,1250,129,539,476,94,11,227, \
427,151,102,126,2176,71,297,60,413,195, \
190,944,49,554,1102,676,279,78,143,364, \
357,462,1144,1050,218,423,623,364,416,239, \
143,280,248,365,77,77,1529,157,361,514, \
536,31,330,87,193,514,935,227,18,91, \
104,49,133,1149,104,518,396,1015,143,445, \
360,385,680,49,1053,669,647,931,140,231, \
31,1075,483,627,101,1012,714,346,504,60, \
917,1140,1180,98,297,1029,225,1918,406,188, \
368,466,1305,1117,1028,50,150,273,333,101, \
151,146,1100,119,1532,497,487,235,658,322, \
538,210,701,574,136,220,168,105,603,332, \
409,84,81,39,860,309,384,259,266,207, \
872,377,403,248,819,882,931,148,42,371, \
805,325,668,529,409,3151,2016,14,38,1487, \
350,295,266,343,1833,1887,123,370,260,696, \
137,962,410,132,847,1051,426,39,214,546, \
539,493,325,137,112,889,130,237,43,1183, \
118,371,1,580,316,434,2698,53,98,262, \
203,119,31,189,813,119,195,294,1435,1345, \
531,624,210,231,321,553,11,756,1358)
import bisect
tbl = [0]*MAX
for i in range(1, MAX): tbl[i] = tbl[i-1] + diff[i]
for i in range(MAX): tbl[i] = tbl[i]*30+19
while 1:
n = int(input())
if n == 0: break
if n < 19: print("13")
else:
p = bisect.bisect_left(tbl, n)
if tbl[p] == n: print(n)
else: print(tbl[p-1])
``` | output | 1 | 7,436 | 22 | 14,873 |
Provide a correct Python 3 solution for this coding contest problem.
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 β€ n β€ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439 | instruction | 0 | 7,437 | 22 | 14,874 |
"Correct Solution:
```
# AOJ 0222 Prime Quadruplet
# Python3 2018.6.23 bal4u
# From Wekipedia (https://en.wikipedia.org/wiki/Prime_quadruplet)
# All prime quadruplets except {5, 7, 11, 13} are of the form
# {30n + 11, 30n + 13, 30n + 17, 30n + 19} for some integer n.
MAX = 899
diff = (0,3,3,21,22,13,7,39,7,73, \
126,119,88,3,11,66,29,17,53,42, \
101,214,104,298,252,133,255,141,76,91, \
168,81,45,56,203,301,43,66,291,223, \
92,97,442,290,437,281,38,144,549,241, \
29,192,11,518,266,490,122,130,13,329, \
85,209,71,241,290,18,301,52,120,34, \
50,805,276,217,182,53,209,155,77,468, \
448,29,90,85,91,7,146,21,309,234, \
60,213,511,59,273,364,57,77,87,231, \
452,168,154,346,273,588,11,91,322,335, \
140,221,87,442,297,95,321,498,146,182, \
8,38,11,679,111,120,83,36,59,462, \
32,349,448,333,644,63,101,960,161,759, \
255,354,270,52,200,133,112,297,298,27, \
74,577,25,182,280,584,756,266,287,277, \
119,31,561,59,179,630,34,98,1,84, \
217,234,4,48,127,528,679,35,108,15, \
752,60,31,228,559,7,35,56,43,10, \
151,374,297,294,14,60,196,133,18,63, \
63,17,35,290,953,584,66,102,427,4, \
357,507,441,420,802,14,66,171,252,88, \
14,364,32,220,66,256,427,651,52,287, \
987,214,161,319,241,1333,190,325,63,500, \
1026,60,13,112,238,144,137,349,417,32, \
164,196,115,735,200,382,273,104,119,214, \
665,235,297,665,25,34,211,280,542,375, \
188,42,134,573,350,106,17,112,676,1095, \
403,62,193,60,13,116,60,255,609,350, \
7,165,661,25,748,176,10,283,144,987, \
389,59,60,342,112,144,31,98,676,297, \
652,189,56,34,441,50,314,266,29,546, \
297,39,657,46,703,70,270,221,122,767, \
13,134,318,1222,84,650,371,92,164,760, \
318,175,158,679,496,389,273,38,676,270, \
902,228,143,196,18,287,102,409,612,1, \
56,269,311,714,1092,176,34,165,143,438, \
266,249,97,442,105,7,913,81,80,871, \
497,585,574,11,220,94,855,132,473,836, \
301,7,833,63,1145,60,1886,382,111,43, \
111,319,431,108,297,60,878,799,133,472, \
529,420,241,46,231,304,616,1145,595,447, \
589,76,399,865,154,101,119,739,528,673, \
49,994,412,1072,6,25,3,49,126,1079, \
1141,66,220,932,1049,561,692,764,476,248, \
200,1897,658,644,24,399,143,1331,839,1, \
1077,760,11,34,658,36,647,21,528,242, \
98,529,24,1117,192,396,930,224,365,66, \
557,377,757,322,203,335,770,155,97,21, \
665,484,553,321,207,116,574,272,287,253, \
637,259,38,263,62,1268,451,693,756,630, \
357,105,32,581,455,153,540,350,91,210, \
409,270,377,442,490,615,424,52,890,199, \
102,1746,462,749,24,644,540,220,840,1656, \
223,74,434,179,665,923,428,307,875,50, \
2387,276,109,363,529,550,139,798,176,150, \
297,123,66,266,414,17,130,1344,300,1799, \
8,1176,279,351,461,396,112,626,498,931, \
2782,123,1253,780,781,1119,46,39,847,468, \
1037,1144,63,332,294,1082,525,459,220,70, \
231,31,1029,256,290,662,242,98,252,13, \
1008,64,346,1211,119,802,189,272,298,122, \
697,319,195,273,410,1221,365,885,322,52, \
847,165,112,67,812,630,801,87,60,424, \
630,867,231,123,308,396,76,119,60,203, \
17,63,553,931,147,588,127,437,164,43, \
14,371,115,150,354,315,473,3,1221,245, \
36,272,214,24,385,249,182,445,171,35, \
921,300,1558,1250,129,539,476,94,11,227, \
427,151,102,126,2176,71,297,60,413,195, \
190,944,49,554,1102,676,279,78,143,364, \
357,462,1144,1050,218,423,623,364,416,239, \
143,280,248,365,77,77,1529,157,361,514, \
536,31,330,87,193,514,935,227,18,91, \
104,49,133,1149,104,518,396,1015,143,445, \
360,385,680,49,1053,669,647,931,140,231, \
31,1075,483,627,101,1012,714,346,504,60, \
917,1140,1180,98,297,1029,225,1918,406,188, \
368,466,1305,1117,1028,50,150,273,333,101, \
151,146,1100,119,1532,497,487,235,658,322, \
538,210,701,574,136,220,168,105,603,332, \
409,84,81,39,860,309,384,259,266,207, \
872,377,403,248,819,882,931,148,42,371, \
805,325,668,529,409,3151,2016,14,38,1487, \
350,295,266,343,1833,1887,123,370,260,696, \
137,962,410,132,847,1051,426,39,214,546, \
539,493,325,137,112,889,130,237,43,1183, \
118,371,1,580,316,434,2698,53,98,262, \
203,119,31,189,813,119,195,294,1435,1345, \
531,624,210,231,321,553,11,756,1358)
def bsch(x):
l, r = 0, MAX
while l < r:
m = (l + r) >> 1
if tbl[m] == x: return m
if tbl[m] < x: l = m+1
else: r = m
return l-1;
tbl = [0]*MAX
for i in range(1, MAX): tbl[i] = tbl[i-1] + diff[i]
for i in range(MAX): tbl[i] = tbl[i]*30+19
while 1:
n = int(input())
if n == 0: break
if n < 19: print("13")
else: print(tbl[bsch(n)])
``` | output | 1 | 7,437 | 22 | 14,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 β€ n β€ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439
Submitted Solution:
```
primes = [0, 0] + [1]*999999
for i in range(2, 1001):
for j in range(i*i, 1000001, i):
primes[j] = 0
while True:
n = int(input())
if n == 0:
break
for i in range(5, n+1)[::-1]:
if primes[i] and primes[i-2] and primes[i-6] and primes[i-8]:
print(i)
break
``` | instruction | 0 | 7,438 | 22 | 14,876 |
No | output | 1 | 7,438 | 22 | 14,877 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 β€ n β€ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439
Submitted Solution:
```
def get_quad(n, p):
for ni in range(n,0,-1):
if p[ni] and p[ni - 2] and p[ni - 6] and p[ni - 8]:
return ni
def sieve():
n = 10000001
p = [1] * n
p[0] = p[1] = 0
for i in range(int(n ** 0.5)):
if p[i]:
for j in range(2 * i, len(p), i):
p[j] = 0
return p
import sys
f = sys.stdin
prime = sieve()
while True:
n = f.readline()
if not n.isnumeric():
continue
n = int(n)
if n == 0:
break
print(get_quad(ni, prime))
``` | instruction | 0 | 7,439 | 22 | 14,878 |
No | output | 1 | 7,439 | 22 | 14,879 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 β€ n β€ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439
Submitted Solution:
```
def get_quad(n, p):
return 0
def sieve():
n = 10000001
p = [1] * n
p[0] = p[1] = 0
for i in range(int(n ** 0.5)):
if p[i]:
for j in range(2 * i, len(p), i):
p[j] = 0
return p
import sys
f = sys.stdin
prime = sieve()
while True:
ni = int(f.readline())
if ni == 0:
break
print(get_quad(ni, prime))
``` | instruction | 0 | 7,440 | 22 | 14,880 |
No | output | 1 | 7,440 | 22 | 14,881 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 β€ n β€ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439
Submitted Solution:
```
primes = [0, 0] + [1] * 9999999
for i in range(2, 3163):
if primes[i]:
for j in range(i*i, 10000001, i):
primes[j] = 0
while True:
n = int(input())
if n == 0:
break
for i in range(5, n+1)[::-1]:
if primes[i-8] & primes[i-6] & primes[i-2] & primes[i]):
print(i)
break
``` | instruction | 0 | 7,441 | 22 | 14,882 |
No | output | 1 | 7,441 | 22 | 14,883 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,719 | 22 | 15,438 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
t=int(input())
for i in range(t):
l,r=map(int,input().split())
rem=r%l
if (r-rem)!=l:
print(l,r-rem)
else:
print(-1,-1)
``` | output | 1 | 7,719 | 22 | 15,439 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,720 | 22 | 15,440 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
t = int(input())
while(t!=0):
temp = input()
l,r = temp.split()
l = int(l)
r = int(r)
x = -1
y = -1
if r>= 2*l:
x, y = l, 2*l
print(x,y)
t-=1
``` | output | 1 | 7,720 | 22 | 15,441 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,721 | 22 | 15,442 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
from collections import Counter
tests = int(input())
for _ in range(tests):
l, r = map(int, input().split())
# arr = [int(a) for a in input().strip().split(' ')]
x = l
y = 2*l
if y <= r:
print(x, y)
else:
print(-1, -1)
``` | output | 1 | 7,721 | 22 | 15,443 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,722 | 22 | 15,444 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
def calcMinorLCM(a, b, results):
if b < a*2:
results.append(-1)
results.append(-1)
else:
results.append(a)
results.append(a*2)
t = int(input())
results = []
for i in range(t):
[a, b] = list(map(int, input().split(' ')))
calcMinorLCM(a, b, results)
for i in range(int(len(results)/2)):
print(results[2*i], results[2*i+1])
``` | output | 1 | 7,722 | 22 | 15,445 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,723 | 22 | 15,446 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
t = int(input())
for _ in range(t):
l, r = [int(s) for s in input().split()]
if r < l + l:
print(-1, -1)
else:
print(l, l + l)
``` | output | 1 | 7,723 | 22 | 15,447 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,724 | 22 | 15,448 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
t=int(input())
for _ in range(t):
l,r=map(int,input().split())
if r>=2*l:
print(l,2*l)
else:
print(-1,-1)
``` | output | 1 | 7,724 | 22 | 15,449 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,725 | 22 | 15,450 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
t = int(input())
for _ in range(t):
l,r = map(int, input().split())
x, y = l, l*2
if y > r:
print(-1, -1)
else:
print(x, y)
``` | output | 1 | 7,725 | 22 | 15,451 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1 | instruction | 0 | 7,726 | 22 | 15,452 |
Tags: constructive algorithms, greedy, math, number theory
Correct Solution:
```
for _ in range(int(input())):
L, R = map(int, input().split())
if 2*L > R:
print(-1, -1)
else:
print(L, 2*L)
``` | output | 1 | 7,726 | 22 | 15,453 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
from math import *
sInt = lambda: int(input())
mInt = lambda: map(int, input().split())
lInt = lambda: list(map(int, input().split()))
t = sInt()
for _ in range(t):
n,m = mInt()
if 2*n<=m:
print(n,2*n)
else:
print(-1,-1)
``` | instruction | 0 | 7,727 | 22 | 15,454 |
Yes | output | 1 | 7,727 | 22 | 15,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def print_list(l):
print(' '.join(map(str,l)))
# import heapq as hq
# import bisect as bs
# from collections import deque as dq
# from collections import defaultdict as dc
# from math import ceil,floor,sqrt
# from collections import Counter
for _ in range(N()):
l,r = RL()
if r<l*2:
print(-1,-1)
else:
print(l,l*2)
``` | instruction | 0 | 7,728 | 22 | 15,456 |
Yes | output | 1 | 7,728 | 22 | 15,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
for _ in range(int(input())):
l,r=map(int,input().split())
c=0
while 2*l<r+1:
if 2*l<=r:
print(l,l*2)
c=1
break
l+=1
if c==0:
print("-1 -1")
``` | instruction | 0 | 7,729 | 22 | 15,458 |
Yes | output | 1 | 7,729 | 22 | 15,459 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
for s in[*open(0)][1:]:l,r=map(int,s.split());print(*([l,2*l],[-1]*2)[r<2*l])
``` | instruction | 0 | 7,730 | 22 | 15,460 |
Yes | output | 1 | 7,730 | 22 | 15,461 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
for i in range (int(input())):
m,n=map(int,input().split())
if n%m==0:
print(m,n)
elif (m+1)*2 <=n:
print(m+1,(m+1)*2)
else:
print(-1,-1)
``` | instruction | 0 | 7,731 | 22 | 15,462 |
No | output | 1 | 7,731 | 22 | 15,463 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
import math
for i in range(int(input())):
a,b=map(int,input().split())
if a%2==0:
x=a
y=a+1
else:
x=a+1
y=a+2
while y<=b:
if (x*y)//math.gcd(x,y)<=b:
print(x,y)
break
if y>=b:
print("-1","-1")
break
else:
y+=1
``` | instruction | 0 | 7,732 | 22 | 15,464 |
No | output | 1 | 7,732 | 22 | 15,465 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
t = int(input())
def gcd(a, b):
while b != 0:
t = b
b = a % b
a = t
return a
def lcm(x, y):
return x / gcd(x, y) * y
for kkk in range(t):
s = [int(i) for i in input().split()]
l, r = s[0], s[1]
x = l
y = x + 1
while 1:
if lcm(x, y) > r:
y+=1
if y > (l+r)//2 + 1:
x+=1
y = x + 1
else:
print(x, y)
break
if x>(l+r)//2:
print("-1 -1")
break
``` | instruction | 0 | 7,733 | 22 | 15,466 |
No | output | 1 | 7,733 | 22 | 15,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let LCM(x, y) be the minimum positive integer that is divisible by both x and y. For example, LCM(13, 37) = 481, LCM(9, 6) = 18.
You are given two integers l and r. Find two integers x and y such that l β€ x < y β€ r and l β€ LCM(x, y) β€ r.
Input
The first line contains one integer t (1 β€ t β€ 10000) β the number of test cases.
Each test case is represented by one line containing two integers l and r (1 β€ l < r β€ 10^9).
Output
For each test case, print two integers:
* if it is impossible to find integers x and y meeting the constraints in the statement, print two integers equal to -1;
* otherwise, print the values of x and y (if there are multiple valid answers, you may print any of them).
Example
Input
4
1 1337
13 69
2 4
88 89
Output
6 7
14 21
2 4
-1 -1
Submitted Solution:
```
def gcd(a,b):
while b > 0:
a, b = b, a % b
return a
def lcm(a, b):
return a * b / gcd(a, b)
n = int(input())
for times in range(n):
l,r = map(int, input().split(" "))
first = l
second = first + 1
last = lcm(first, second)
while last > r:
second += 1
if second > r:
break
last = lcm(first, second)
if second <= r:
print(first,second)
else:
print(str(-1))
``` | instruction | 0 | 7,734 | 22 | 15,468 |
No | output | 1 | 7,734 | 22 | 15,469 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15 | instruction | 0 | 7,843 | 22 | 15,686 |
Tags: math, number theory
Correct Solution:
```
from bisect import bisect_left as bl
from bisect import bisect_right as br
import heapq
import math
from collections import *
from functools import reduce,cmp_to_key
import sys
input = sys.stdin.readline
# M = mod = 998244353
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
# def inv_mod(n):return pow(n, mod - 2, mod)
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n').split(' ')]
def li3():return [int(i) for i in input().rstrip('\n')]
l = [2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011,24036583]
n = val()
curr = l[n-1]-1
print((pow(2,curr)-1)%(10**9 + 7))
``` | output | 1 | 7,843 | 22 | 15,687 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15 | instruction | 0 | 7,844 | 22 | 15,688 |
Tags: math, number theory
Correct Solution:
```
# I've proven, that z takes form of 2 ** (k - 1) - 1,
# where 2 ** k - 1 is prime, which are called 'Mersenne primes'.
p = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127,\
521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689,\
9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503,\
132049, 216091, 756839, 859433, 1257787, 1398269,\
2976221, 3021377, 6972593, 13466917, 20996011]
n = int(input())
MOD = 10 ** 9 + 7
print((pow(2, p[n - 1] - 1, MOD) - 1) % MOD)
``` | output | 1 | 7,844 | 22 | 15,689 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15 | instruction | 0 | 7,845 | 22 | 15,690 |
Tags: math, number theory
Correct Solution:
```
print([0,1,3,15,63,4095,65535,262143,73741816,536396503,140130950,487761805,319908070,106681874,373391776,317758023,191994803,416292236,110940209,599412198,383601260,910358878,532737550,348927936,923450985,470083777,642578561,428308066,485739298,419990027,287292016,202484167,389339971,848994100,273206869,853092282,411696552,876153853,90046024,828945523,697988359][int(input())])
``` | output | 1 | 7,845 | 22 | 15,691 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15 | instruction | 0 | 7,846 | 22 | 15,692 |
Tags: math, number theory
Correct Solution:
```
n=int(input())
p=[2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011]
res=1
for i in range(p[n-1]-1):
res*=2
res%=1000000007
print(res-1)
``` | output | 1 | 7,846 | 22 | 15,693 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15 | instruction | 0 | 7,847 | 22 | 15,694 |
Tags: math, number theory
Correct Solution:
```
mercenes = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667]
print((2**(mercenes[int(input())-1]-1)-1)%1000000007)
``` | output | 1 | 7,847 | 22 | 15,695 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15 | instruction | 0 | 7,848 | 22 | 15,696 |
Tags: math, number theory
Correct Solution:
```
mod = 10**9+7
a = [2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011]
n = int(input())
print(pow(2,a[n-1]-1,mod)-1)
``` | output | 1 | 7,848 | 22 | 15,697 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15
Submitted Solution:
```
a = [1, 2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126, 520, 606, 1278, 2202, 2280, 3216, 4252, 4422, 9688, 9940, 11212, 19936, 21700, 23208, 44496, 86242, 110502, 132048, 216090, 756838, 859432, 1257786, 1398268, 2976220, 3021376, 6972592, 13466916, 20996010, 24036582, 25964950, 30402456, 32582656]
x = int(input());
print(2**a[x - 1] - 1)
``` | instruction | 0 | 7,849 | 22 | 15,698 |
No | output | 1 | 7,849 | 22 | 15,699 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15
Submitted Solution:
```
n=int(input())
p=[2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,13466917,20996011]
res=1
for i in range(p[n-1]-1):
res*=2
res%=1000000007
print(res-1)
``` | instruction | 0 | 7,850 | 22 | 15,700 |
No | output | 1 | 7,850 | 22 | 15,701 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15
Submitted Solution:
```
n = int(input())
k = 1
ans = 1
for j in range(n):
i = j+1
prev_ans = ans%1000000007
k+=2
ans = prev_ans*k
print(prev_ans)
``` | instruction | 0 | 7,851 | 22 | 15,702 |
No | output | 1 | 7,851 | 22 | 15,703 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider the following equation:
<image> where sign [a] represents the integer part of number a.
Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.
Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.
Input
The first line contains a single integer n (1 β€ n β€ 40).
Output
Print a single integer β the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
15
Submitted Solution:
```
n=int(input())
p=[2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011]
print(len(p))
res=1
for i in range(p[n-1]-1):
res*=2
res%=1000000007
print(res-1)
``` | instruction | 0 | 7,852 | 22 | 15,704 |
No | output | 1 | 7,852 | 22 | 15,705 |
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