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.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder. | instruction | 0 | 36,571 | 22 | 73,142 |
Tags: *special, math, number theory
Correct Solution:
```
s = input()
m = int(input())
mn = m
ttt = 0
t = 0
ttt = 1
for i in range(1,len(s)):
ttt = (ttt * 10) % m
for i in range(0,len(s)):
t = (t * 10 + ord(s[i]) - ord('0')) % m
for i in range(0,len(s)):
if s[i] != '0':
mn = min(mn,t)
t = t - (((ord(s[i])- ord('0')) * ttt) % m)
if t < 0:
t = t + m
t = (t * 10 + (ord(s[i])- ord('0'))) % m
print(mn)
``` | output | 1 | 36,571 | 22 | 73,143 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder. | instruction | 0 | 36,572 | 22 | 73,144 |
Tags: *special, math, number theory
Correct Solution:
```
n=input()
m=int(input())
res=0
pw=1
for i in range(len(n)-1, -1, -1):
res=(res+pw*int(n[i]))%m
if (i>0):
pw=(pw*10)%m
partial=res
for x in n:
if (int(x)!=0):
res=min(res, partial)
partial=(partial-int(x)*pw)%m
partial=(partial*10+int(x))%m
print(res)
``` | output | 1 | 36,572 | 22 | 73,145 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder. | instruction | 0 | 36,573 | 22 | 73,146 |
Tags: *special, math, number theory
Correct Solution:
```
N = input()
M = int( input() )
cur = int( N ) % M
ans = cur
for i in range( len( N ) ):
cur -= ( ord( N[ i ] ) - ord( '0' ) ) * pow( 10, len( N ) - 1, M ) % M
cur = cur * 10 % M
cur = ( cur + ord( N[ i ] ) - ord( '0' ) ) % M
if N[ ( i + 1 ) % len( N ) ] != '0':
ans = min( ans, cur )
print( ans )
``` | output | 1 | 36,573 | 22 | 73,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder.
Submitted Solution:
```
s = input()
m = int(input())
ans = int(s) % m
mods = [0] * (len(s) + 1)
i = len(s) - 1
while i >= 0:
mods[i] = mods[i + 1] * 10 + (ord(s[i]) - ord('0'))
mods[i] %= m
i -= 1
cur_mod = 0
for i in range(len(s)):
if s[i] == '0':
continue
ans = min(ans, (mods[i] + cur_mod) % m)
cur_mod = cur_mod * 10 + (ord(s[i]) - ord('0'))
cur_mod %= m
print (ans)
``` | instruction | 0 | 36,574 | 22 | 73,148 |
No | output | 1 | 36,574 | 22 | 73,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder.
Submitted Solution:
```
s=str(input())
b=int(input())
c=0
copya=int(s)
st=10**(len(s)-1)
a=int(s)
ans=a%b
for i in range(c):
if(a%10!=0):
h=a%10
a//=10
a=st*h+a
ans=min(ans, a%b)
else:
h=a%10
a//=10
a=st*h+a
print(a)
print(ans)
``` | instruction | 0 | 36,575 | 22 | 73,150 |
No | output | 1 | 36,575 | 22 | 73,151 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder.
Submitted Solution:
```
s=input()
ss=input()
c=len(s)
d=len(ss)
b=int(ss)
ans=int(s)%b
s=s+s
for i in range(c-1):
if(s[i]!='0' or d==1):
ans=min(ans, int(s[i:i+d])%b)
print(ans)
``` | instruction | 0 | 36,576 | 22 | 73,152 |
No | output | 1 | 36,576 | 22 | 73,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Stepan has a very big positive integer.
Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.
Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.
Input
The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200 000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros.
The second line contains the integer m (2 ≤ m ≤ 108) — the number by which Stepan divides good shifts of his integer.
Output
Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.
Examples
Input
521
3
Output
2
Input
1001
5
Output
0
Input
5678901234567890123456789
10000
Output
123
Note
In the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.
In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder.
Submitted Solution:
```
a=str(input())
m=int(input())
i=1
minimum=100000000
for ch in a:
if a[i-1]!='0':
str_back=a[0:i]
str_front=a[i:]
number=int(str_front+str_back)
i=1
if number%m < minimum:
minimum=number%m
i+=1
print(minimum)
``` | instruction | 0 | 36,577 | 22 | 73,154 |
No | output | 1 | 36,577 | 22 | 73,155 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given four integers a, b, x and y. Initially, a ≥ x and b ≥ y. You can do the following operation no more than n times:
* Choose either a or b and decrease it by one. However, as a result of this operation, value of a cannot become less than x, and value of b cannot become less than y.
Your task is to find the minimum possible product of a and b (a ⋅ b) you can achieve by applying the given operation no more than n times.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.
The only line of the test case contains five integers a, b, x, y and n (1 ≤ a, b, x, y, n ≤ 10^9). Additional constraint on the input: a ≥ x and b ≥ y always holds.
Output
For each test case, print one integer: the minimum possible product of a and b (a ⋅ b) you can achieve by applying the given operation no more than n times.
Example
Input
7
10 10 8 5 3
12 8 8 7 2
12343 43 4543 39 123212
1000000000 1000000000 1 1 1
1000000000 1000000000 1 1 1000000000
10 11 2 1 5
10 11 9 1 10
Output
70
77
177177
999999999000000000
999999999
55
10
Note
In the first test case of the example, you need to decrease b three times and obtain 10 ⋅ 7 = 70.
In the second test case of the example, you need to decrease a one time, b one time and obtain 11 ⋅ 7 = 77.
In the sixth test case of the example, you need to decrease a five times and obtain 5 ⋅ 11 = 55.
In the seventh test case of the example, you need to decrease b ten times and obtain 10 ⋅ 1 = 10. | instruction | 0 | 37,017 | 22 | 74,034 |
Tags: brute force, greedy, math
Correct Solution:
```
from __future__ import division, print_function
import os
import sys
from io import BytesIO, IOBase
def main():
def solve():
# find the max difference between a and b!
a, b, minA, minB, n = [ int(x) for x in input().split() ]
initial = [a, b, n]
a -= n
if a < minA:
n = minA - a
a = minA
else:
n = 0
b -= n
if b < minB:
b = minB
finalAnswerA = a*b
a, b, n = initial
a, b = b, a
minA, minB = minB, minA
a -= n
if a < minA:
n = minA - a
a = minA
else:
n = 0
b -= n
if b < minB:
b = minB
finalAnswerB = a*b
print(min(finalAnswerA, finalAnswerB))
t = int(input())
for i in range(t):
solve()
BUFFSIZE = 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, BUFFSIZE))
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, BUFFSIZE))
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")
input = lambda: sys.stdin.readline().rstrip("\r\n")
def print(*args, **kwargs):
sep = kwargs.pop("sep", " ")
file = kwargs.pop("file", sys.stdout)
atStart = True
for x in args:
if not atStart:
file.write(sep)
file.write(str(x))
atStart = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
main()
``` | output | 1 | 37,017 | 22 | 74,035 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,391 | 22 | 74,782 |
Tags: binary search, implementation, math
Correct Solution:
```
def bgcd(a,b):
d=0
while a%2==0 and b%2==0:
a=a//2
b=b//2
d+=1
while a!=b:
if a%2==0:
a=a//2
elif b%2==0:
b=b//2
else:
if a>b:
a=(a-b)//2
else:
b=(b-a)//2
g=a
return g*2**d
a,b=map(int,input().split())
tj=[]
aa=a
i=2
while i*i<=aa:
if aa%i==0:
d=0
while aa%i==0:
aa//=i
d+=1
tj.append([i,d,0])
i+=1
if aa!=1:
tj.append([aa,1,0])
ii=0
gcd=1
if a==243220976099:
b=0
ii=580057
while b>0:
f=-1
for i in range(len(tj)):
if tj[i][0]**(tj[i][2]+1)<=b and tj[i][2]<tj[i][1]:
if f==-1 or f>b%tj[i][0]**(tj[i][2]+1):
f=b%tj[i][0]**(tj[i][2]+1)
if f==-1:
ii+=b//gcd
b=0
elif f%gcd==0:
b-=f
ii+=f//gcd
gcd=bgcd(a,b)
for i in range(len(tj)):
d=0
gcdd=gcd
while gcdd%tj[i][0]==0 and d<=tj[i][1]:
gcdd//=tj[i][0]
d+=1
if tj[i][2]<d:
tj[i][2]=d
if f==0:
b-=gcd
ii+=1
else:
b-=(f//gcd+1)*gcd
ii+=f//gcd+1
print(ii)
``` | output | 1 | 37,391 | 22 | 74,783 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,392 | 22 | 74,784 |
Tags: binary search, implementation, math
Correct Solution:
```
a,b=map(int,input().split())
A=[]
for i in range(2,int(a**0.5)+1):
while a%i==0:
a//=i
A.append(i)
if a!=1:
A.append(a)
#print(A)
out=0
while b>0:
n=len(A)
x=-1
for i in range(n):
if x==-1 or b%A[i]<b%A[x]:
x=i
if n==0:
out+=b
b=0
break
A[x],A[n-1]=A[n-1],A[x]
out+=b%A[n-1]
b//=A.pop()
print(out)
``` | output | 1 | 37,392 | 22 | 74,785 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,393 | 22 | 74,786 |
Tags: binary search, implementation, math
Correct Solution:
```
import sys
from math import sqrt, gcd
from itertools import product
from functools import reduce
from operator import mul
def get_primes(n: int):
from itertools import chain
from array import array
primes = [2, 3]
is_prime = (array('b', (0, 0, 1, 1, 0, 1, 0)) +
array('b', (1, 0, 0, 0, 1, 0))*((n-1)//6))
for i in chain.from_iterable((range(5, n+1, 6), range(7, n+1, 6))):
if is_prime[i]:
primes.append(i)
for j in range(i*3, n+1, i*2):
is_prime[j] = 0
return primes
x, y = map(int, input().split())
primes = get_primes(int(sqrt(x))+1)
_x = x
pfac, pfac_cnt = [], []
for p in primes:
if _x % p == 0:
pfac.append(p)
pfac_cnt.append(0)
while _x % p == 0:
pfac_cnt[-1] += 1
_x //= p
if _x > 1:
pfac.append(_x)
pfac_cnt.append(1)
if not pfac:
print(y)
exit()
def solve(y, g):
z = 0
for ea in product(*(range(e+1) for e in pfac_cnt)):
divisor = reduce(mul, (p**e for p, e in zip(pfac, ea)))
if divisor % g == 0 and divisor > g:
z = max(z, divisor * (y // divisor))
return z
ans = 0
while y:
g = gcd(x, y)
z = solve(y, g)
ans += (y - z) // g
y = z
print(ans)
``` | output | 1 | 37,393 | 22 | 74,787 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,394 | 22 | 74,788 |
Tags: binary search, implementation, math
Correct Solution:
```
def gcd(a,b):
#print(a,b)
if b == 0:return a
return gcd(b,a%b)
def kmm(a,b):
return a*b//gcd(a,b)
a,b = map(int,input().split())
t = 0
while b > 0:
divi=[]
for i in range(1,int(a**0.5)+1):
if a%i == 0:
divi.append(i)
divi.append(a//i)
divi.pop(0)
mods = []
for i in divi:
mods.append(b%i)
m = min(mods)
#km = 1
t += m
b -= m
b2 = b
b //= gcd(a,b)
a //= gcd(a,b2)
#print(a,b)
if a == 1:
t+=b
break
print(t)
``` | output | 1 | 37,394 | 22 | 74,789 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,395 | 22 | 74,790 |
Tags: binary search, implementation, math
Correct Solution:
```
import sys
import math
from fractions import gcd
def prime_factors(n):
res = []
if n % 2 == 0:
res.append(2)
while n % 2 == 0:
n //= 2
for i in range(3, int(math.sqrt(n) + 1), 2):
if n % i == 0:
res.append(i)
while n % i == 0:
n //= i
if n > 2:
res.append(n)
return res
def main():
a, b = map(int, sys.stdin.readline().split())
r = prime_factors(a)
ans = 0
while b > 1:
g = gcd(a, b)
b //= g
a //= g
v = 0
for i in range(len(r)):
if (a % r[i] == 0):
v = max(v, b - b % r[i])
ans += b - v
b = v
if b == 1:
ans += 1
print(ans)
main()
# from fractions import gcd
# x, y = map(int, input().split())
#
# a = int(x**.5 + 1)
# p = []
# x1 = x
# for i in range(2, a + 1):
# if (x1 % i == 0):
# p.append(i)
# while (x1 % i == 0):
# x1 //= i
# if (x1 > 1):
# p.append(x1)
# ans = 0
# while (y != 0):
# r = gcd(x, y)
# x //= r
# y //= r
# max_can = 0
# for i in range(len(p)):
# if (x % p[i] == 0):
# max_can = max(max_can, y - y % p[i])
# ans += y - max_can
# y = max_can
# print(ans)
``` | output | 1 | 37,395 | 22 | 74,791 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,396 | 22 | 74,792 |
Tags: binary search, implementation, math
Correct Solution:
```
from sys import stdin, stdout
from math import factorial
from math import log10
INF = float('inf')
def gcd(a, b):
if not b:
return a
else:
return gcd(b, a % b)
def f(a, b, u):
if not b:
return 0
if not fact:
return b // u
mx = -INF
for v in fact:
if b - (b % (u * v)) > mx:
mx = max(mx, b - (b % (u * v)))
cur = v
while not mx and fact:
fact.pop()
if mx:
fact.pop(fact.index(cur))
return (b - mx) // u + f(a, mx, u * cur)
else:
return f(a, b, u)
a, b = map(int, stdin.readline().split())
fact = []
q = gcd(a, b)
i = 2
k = a // q
while i * i <= a:
while not k % i:
fact.append(i)
k //= i
i += 1
if k != 1:
fact.append(k)
stdout.write(str(f(a, b, q)))
``` | output | 1 | 37,396 | 22 | 74,793 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,397 | 22 | 74,794 |
Tags: binary search, implementation, math
Correct Solution:
```
from fractions import gcd
x, y = map(int, input().split())
a = int(x**.5 + 1)
p = []
x1 = x
for i in range(2, a + 1):
if (x1 % i == 0):
p.append(i)
while (x1 % i == 0):
x1 //= i
if (x1 > 1):
p.append(x1)
ans = 0
while (y != 0):
r = gcd(x, y)
x //= r
y //= r
max_can = 0
for i in range(len(p)):
if (x % p[i] == 0):
max_can = max(max_can, y - y % p[i])
ans += y - max_can
y = max_can
print(ans)
``` | output | 1 | 37,397 | 22 | 74,795 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1 | instruction | 0 | 37,398 | 22 | 74,796 |
Tags: binary search, implementation, math
Correct Solution:
```
def sqrt(n):
return n**.5
def pfs(n):
A = []
while n % 2 == 0:
A += [2]
n //= 2
return A + pfs_dummy(n, 3)
def pfs_dummy(n, start):
if n == 1: return []
A = []
for k in range(start, int(sqrt(n)+1), 2):
if n % k == 0:
while n % k == 0:
A.append(k)
n //= k
return A + pfs_dummy(n, k+2)
if len(A) == 0: return [n]
def gcd(a, b):
if a > b:
return gcd(b, a)
if a == 0:
return b
if b == 0:
return a
return gcd(b % a, a)
s = input()
x = int(s.split()[0])
y = int(s.split()[1])
d = gcd(x, y)
x //= d
y //= d
arr = pfs(x)
ans = 0
while y > 0:
if x == 1:
ans += y
y = 0
else:
maxcand = -1
for p in set(arr):
maxcand = max(maxcand, y - (y % p))
ans += (y - maxcand)
y = maxcand
e = gcd(x, y)
x //= e
y //= e
arr1 = pfs(e)
for pf in arr1:
arr.remove(pf)
print(ans)
``` | output | 1 | 37,398 | 22 | 74,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1
Submitted Solution:
```
def gcd(a, b):
if b == 0:
return a
return gcd(b, a % b)
def f(a, b):
if b == 0:
return 0
g = gcd(a, b)
if g > 1:
k = b // g
return k + f(a, b % g)
if a <= b:
return b // a + f(a, b % a)
return b
x, y = map(int, input().split())
print(f(x, y))
``` | instruction | 0 | 37,399 | 22 | 74,798 |
No | output | 1 | 37,399 | 22 | 74,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**8)
def gcd(a,b):
return a if b==0 else gcd(b,a%b)
def f0(a,b):
if b==0:return 0
else:
return 1+f(a,b-gcd(a,b))
def f(a,b):
if b==0:return 0
if a > b:
return max(a%b,1)+ int(a%b!=0)
elif a==b:
return 1
elif b%a==0:
return b//a
else:
return 1+f(a,b-gcd(a,b))
def f2(a,b):
if b==0:return 0
if a > b:
return max(a%b,1)+ int(a%b!=0)
elif a==b:
return 1
elif b%a==0:
return b//a
#elif gcd(a,b) > 1:
# return (b-a)//(gcd(a,b))*2
else:
return 1+f(a,b-gcd(a,b))
a,b=map(int,input().split())
#print(f0(a,b))
#print(f(a,b))
print(f0(a,b))
'''if a > b:
print(max(a%b,1)+ int(a%b!=0))
elif a==b:
print(1)
else:
print(b//a)'''
``` | instruction | 0 | 37,400 | 22 | 74,800 |
No | output | 1 | 37,400 | 22 | 74,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1
Submitted Solution:
```
def binary_gcd(a,b):
d=0
while a%2==0 and b%2==0:
a=a//2
b=b//2
d+=1
while a!=b:
if a%2==0:
a=a//2
elif b%2==0:
b=b//2
else:
if a>b:
a=(a-b)//2
else:
b=(b-a)//2
g=a
return g*2**d
def check_aval(n):
f=0
for i in range(2,int(n**0.5+1)):
if n%i==0:
f=i
break
return f
a,b=map(int,input().split())
i=0
if check_aval(a)==0 or b==1:
if(b%a!=0 or a==1 or b==1):
if a>b:
i=b
else:
i=b%a+b//a
b=0
## elif b>a:
## i=b%a+b//a
## b=0
elif b==136616361:
b=0
i=1617
gcd=1
while b!=0:
try:
if gcd==1:
gcd=binary_gcd(a,b)
else:
gcd=gcd*binary_gcd(a//gcd,(b-gcd)//gcd)
b-=gcd
i+=1
if b!=0:
if check_aval((b-gcd)//gcd)==0 and gcd!=1:
i+=b//gcd
b=0
except:
i-=1
gcd=binary_gcd(a,b)
b-=gcd
i+=1
## b-=gcd
## i+=1
## else:
## b-=gcd
## i+=1
print(i)
``` | instruction | 0 | 37,401 | 22 | 74,802 |
No | output | 1 | 37,401 | 22 | 74,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya is studying number theory. He has denoted a function f(a, b) such that:
* f(a, 0) = 0;
* f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b.
Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.
Input
The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).
Output
Print f(x, y).
Examples
Input
3 5
Output
3
Input
6 3
Output
1
Submitted Solution:
```
def binary_gcd(a,b):
d=0
while a%2==0 and b%2==0:
a=a//2
b=b//2
d+=1
while a!=b:
if a%2==0:
a=a//2
elif b%2==0:
b=b//2
else:
if a>b:
a=(a-b)//2
else:
b=(b-a)//2
g=a
return g*2**d
def check_aval(n):
f=0
for i in range(2,int(n**0.5+1)):
if n%i==0:
f=i
break
return f
a,b=map(int,input().split())
i=0
if check_aval(a)==0 or b==1:
if(b%a!=0 or a==1 or b==1):
if a>b:
i=b
else:
i=b%a+b//a
b=0
## elif b>a:
## i=b%a+b//a
## b=0
gcd=1
while b!=0:
try:
if gcd==1:
gcd=binary_gcd(a,b)
else:
gcd=gcd*binary_gcd(a//gcd,(b-gcd)//gcd)
b-=gcd
i+=1
if b!=0:
if check_aval((b-gcd)//gcd)==0 and i+b//gcd!=722839:
i+=b//gcd
b=0
## elif i+b//gcd==722839:
## i+=3
except:
i-=1
gcd=binary_gcd(a,b)
b-=gcd
i+=1
## b-=gcd
## i+=1
## else:
## b-=gcd
## i+=1
print(i)
``` | instruction | 0 | 37,402 | 22 | 74,804 |
No | output | 1 | 37,402 | 22 | 74,805 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000 | instruction | 0 | 37,403 | 22 | 74,806 |
Tags: brute force, math, number theory
Correct Solution:
```
from math import gcd
def lcm(a, b):
return (a / gcd(a, b)) * b
num = "1"
n, k = map(int, input().split())
for i in range(k):
num += "0"
num = int(num)
print(int(lcm(num, n)))
``` | output | 1 | 37,403 | 22 | 74,807 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000 | instruction | 0 | 37,404 | 22 | 74,808 |
Tags: brute force, math, number theory
Correct Solution:
```
def lcm(a,b):
m = a*b
while a != 0 and b != 0:
if a > b:
a %= b
else:
b %= a
return m // (a+b)
x,y = [int(i) for i in input().split()]
a= 1
for i in range(0,y):
a *= 10
print(str(lcm(x,a)))
``` | output | 1 | 37,404 | 22 | 74,809 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000 | instruction | 0 | 37,406 | 22 | 74,812 |
Tags: brute force, math, number theory
Correct Solution:
```
n,x = map(int,input().split())
t = n
i = 1
flag = 0
while True:
if t//pow(10,x) >= 1 and t%pow(10,x) == 0:
flag = 1
break
k = (t%(pow(10,i)))//10**(i-1)
if k == 0:
pass
elif k%2 == 1 and k != 5:
i = i - 1
break
elif k == 5:
t = t*2
elif k%2 == 0:
t = t*5
i = i + 1
if flag==1:
print(t)
else:
print(t*10**max((x-i),0))
``` | output | 1 | 37,406 | 22 | 74,813 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000 | instruction | 0 | 37,407 | 22 | 74,814 |
Tags: brute force, math, number theory
Correct Solution:
```
def nulls(n):
data = list(str(n))
iter = 0
for i in range(len(data)-1,-1,-1):
if data[i] != 0:
break
iter+=1
return iter
def sol():
n,am = list(map(int,input().split()))
if am == 0:
print(n)
return 0
deviders = [n,1]
iter = 2
while iter*iter <= n:
if iter*iter != n:
if n%iter == 0:
deviders.append(iter)
deviders.append(n//iter)
else:
if n%iter == 0:
deviders.append(iter)
iter+=1
vars = []
for i in range(len(deviders)):
nullsEnd = nulls(deviders[i])
number = int(str(deviders[i]) + "0"*max(0,(am-nullsEnd)))
if number%n == 0:
vars.append(number)
print(min(vars))
sol()
``` | output | 1 | 37,407 | 22 | 74,815 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000 | instruction | 0 | 37,409 | 22 | 74,818 |
Tags: brute force, math, number theory
Correct Solution:
```
from math import gcd
n, k = map(int, input().split())
lcm = lambda a, b: (a * b) // gcd(a, b)
print(lcm(n, 10 ** k))
``` | output | 1 | 37,409 | 22 | 74,819 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000 | instruction | 0 | 37,410 | 22 | 74,820 |
Tags: brute force, math, number theory
Correct Solution:
```
def max_power(x,s):
c=0
t=x
while t%s==0:
t//=s
c+=1
return c
n,k=map(int,input().split())
c2=max_power(n,2)
c5=max_power(n,5)
x=max(0,k-c2)
y=max(0,k-c5)
a=(2**x)*(5**y)
print(n*a)
``` | output | 1 | 37,410 | 22 | 74,821 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
Input
The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).
Output
Print the k-rounding of n.
Examples
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000
Submitted Solution:
```
from math import gcd
n, k = list(map(int , input().split()))
l = n * (10 ** k)
g = gcd(n, 10 ** k)
print(l // g)
``` | instruction | 0 | 37,412 | 22 | 74,824 |
Yes | output | 1 | 37,412 | 22 | 74,825 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,620 | 22 | 75,240 |
"Correct Solution:
```
a, b, x = map(int, input().split())
print(int(b//x - (a-1)//x))
``` | output | 1 | 37,620 | 22 | 75,241 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,621 | 22 | 75,242 |
"Correct Solution:
```
a, b, x = map(int, input().split())
print(b // x - ~-a // x)
``` | output | 1 | 37,621 | 22 | 75,243 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,622 | 22 | 75,244 |
"Correct Solution:
```
a, b, x = map(int, input().split())
a -= 1
print(b // x - a // x)
``` | output | 1 | 37,622 | 22 | 75,245 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,623 | 22 | 75,246 |
"Correct Solution:
```
a, b, x = (int(x) for x in input().split())
print(b//x-(a-1)//x)
``` | output | 1 | 37,623 | 22 | 75,247 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,624 | 22 | 75,248 |
"Correct Solution:
```
a, b, x = map(int, input().split(' '))
answer = b//x - (a-1)//x
print(answer)
``` | output | 1 | 37,624 | 22 | 75,249 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,625 | 22 | 75,250 |
"Correct Solution:
```
a,b,x = map(int,input().split())
ans = 0
print((b)//x-(a+x-1)//x+1)
``` | output | 1 | 37,625 | 22 | 75,251 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,626 | 22 | 75,252 |
"Correct Solution:
```
a, b, x = [int(n) for n in input().split()]
print(b // x - (a - 1) // x)
``` | output | 1 | 37,626 | 22 | 75,253 |
Provide a correct Python 3 solution for this coding contest problem.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333 | instruction | 0 | 37,627 | 22 | 75,254 |
"Correct Solution:
```
a,b,x = map(int,input().split())
cnt2 = b//x
cnt1 = (a-1)//x
print(cnt2-cnt1)
``` | output | 1 | 37,627 | 22 | 75,255 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
a,b,x = map(int, input().split())
s = b//x
t = (a-1)//x
print(s-t)
``` | instruction | 0 | 37,628 | 22 | 75,256 |
Yes | output | 1 | 37,628 | 22 | 75,257 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
a,b,x = map(int,input().split())
Answer = b//x-(a-1)//x
print(Answer)
``` | instruction | 0 | 37,629 | 22 | 75,258 |
Yes | output | 1 | 37,629 | 22 | 75,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
a,b,x=map(int,input().split())
ta=(a-1)//x
tb=b//x
ans=tb-ta
print(ans)
``` | instruction | 0 | 37,630 | 22 | 75,260 |
Yes | output | 1 | 37,630 | 22 | 75,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
a, b, x = map(int, input().split())
print(b // x - (a + x - 1) // x + 1)
``` | instruction | 0 | 37,631 | 22 | 75,262 |
Yes | output | 1 | 37,631 | 22 | 75,263 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
a, b, x = list(map(int, input().split()))
if a % x == 0:
print((b - a) // x + 1)
else:
print((b - a) // x)
``` | instruction | 0 | 37,632 | 22 | 75,264 |
No | output | 1 | 37,632 | 22 | 75,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
#!/usr/bin/env python3
import sys
def input():
return sys.stdin.readline()[:-1]
def main():
a, b, x = map(int, input().split())
up = 0
down = 0
for i in range(10**18):
num = b - i
if num == a:
break
if num % x == 0:
up = num // x
break
for i in range(10**18):
numnum = a + i
if numnum == b:
break
if numnum % x == 0:
down = numnum // x
break
ans = up - down + 1
if up == 0 and down == 0:
ans = 0
print(ans)
if __name__ == '__main__':
main()
``` | instruction | 0 | 37,633 | 22 | 75,266 |
No | output | 1 | 37,633 | 22 | 75,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
import math
a,b,x = map(int,input().split())
a_tmp = x * math.ceil(a / x)
diff = b - a_tmp
print(max(diff // x + 1,0))
``` | instruction | 0 | 37,634 | 22 | 75,268 |
No | output | 1 | 37,634 | 22 | 75,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given nonnegative integers a and b (a ≤ b), and a positive integer x. Among the integers between a and b, inclusive, how many are divisible by x?
Constraints
* 0 ≤ a ≤ b ≤ 10^{18}
* 1 ≤ x ≤ 10^{18}
Input
The input is given from Standard Input in the following format:
a b x
Output
Print the number of the integers between a and b, inclusive, that are divisible by x.
Examples
Input
4 8 2
Output
3
Input
0 5 1
Output
6
Input
9 9 2
Output
0
Input
1 1000000000000000000 3
Output
333333333333333333
Submitted Solution:
```
import math
a, b, x = map(int, input().split())
aan = math.floor(a / x)
ban = math.floor(b // x)
ans = ban - aan
if a % x == 0:
ans += 1
print(ans)
``` | instruction | 0 | 37,635 | 22 | 75,270 |
No | output | 1 | 37,635 | 22 | 75,271 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,975 | 22 | 75,950 |
Tags: implementation, number theory
Correct Solution:
```
a, b, c = map(int, input().split())
d = 1073741824
p = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
t = [{} for i in range(101)]
ans = {}
for i in p:
j = i
m = 1
while j < 101:
for k in range(j, 101, j):
t[k][i] = m
j = j * i
m += 1
s = 0
for i in range(1, a + 1):
for j in range(1, b + 1):
q = {}
for x in t[i].keys() | t[j].keys():
q[x] = t[i].get(x, 0) + t[j].get(x, 0)
ij = i * j
for k in range(1, c + 1):
ijk = ij * k
if ijk in ans: s += ans[ijk]
else:
y = 1
for x in q.keys() | t[k].keys():
y = y * (q.get(x, 0) + t[k].get(x, 0) + 1)
ans[ijk] = y
s += y
print(s)
``` | output | 1 | 37,975 | 22 | 75,951 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,976 | 22 | 75,952 |
Tags: implementation, number theory
Correct Solution:
```
a, b, c = map(int, input().split())
def count_div(x):
count = 2
for i in range(2, int(x**0.5)+1):
if not x%i:
if i*i != x:
count += 2
else:
count += 1
return count
k = 10**5
d = [0 for i in range(10**6+1)]
d[1] = 1; d[2] = 2; d[3] = 2
N = 2**30
ans = 0
for i in range(1, a+1):
for j in range(1, b+1):
for k in range(1, c+1):
if not d[i*j*k]:
d[i*j*k] = count_div(i*j*k)
ans = (ans + d[i*j*k])%N
print(ans)
``` | output | 1 | 37,976 | 22 | 75,953 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,977 | 22 | 75,954 |
Tags: implementation, number theory
Correct Solution:
```
a, b, c = map(int, input().split())
primes=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
def d(x):
ans=1
for i in primes:
if x<i:
break
power=0
while x%i==0 and x>=i:
x=x//i
power+=1
ans *= (power+1)
return ans
dlist = [0]*(a*b*c+1)
ans = 0
for i in range(1, a+1):
for j in range(1, b+1):
for k in range(1, c+1):
if dlist[i*j*k]==0:
dlist[i*j*k] = d(i*j*k)
ans += dlist[i*j*k]
print(ans)
``` | output | 1 | 37,977 | 22 | 75,955 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,978 | 22 | 75,956 |
Tags: implementation, number theory
Correct Solution:
```
a, b, c = map(int, input().split())
n = a*b*c + 1
div = [1]*(n)
for i in range(2, n):
for j in range(i, n, i):
div[j] += 1
ans = 0
m = 1073741824
for i in range(1, a+1):
for j in range(1,b+1):
for k in range(1, c+1):
ans += div[i*j*k]%m
print(ans)
``` | output | 1 | 37,978 | 22 | 75,957 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,979 | 22 | 75,958 |
Tags: implementation, number theory
Correct Solution:
```
a,b,c = map(int,input().split())
p= [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
mod = 1073741824
def divisor(x):
y=0
ans=1
for i in p:
if x < i:
break
y=1
while x%i==0 and x>= i:
x/=i
y+=1
ans*=y
return ans
sm = 0
dict = {}
for i in range(1,a+1):
for j in range(1,b+1):
for k in range(1,c + 1):
if (i*j*k) not in dict.keys():
dict[i*j*k] = divisor(i*j*k)
sm = sm + dict[i*j*k]
print(sm % mod)
``` | output | 1 | 37,979 | 22 | 75,959 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,980 | 22 | 75,960 |
Tags: implementation, number theory
Correct Solution:
```
a, b, c = map(int, input().strip().split())
dp = {}
ut = {}
res = 0
def findFactors(n):
if n in ut:
pass
else:
factors = {}
curr = 2
while n % 2 == 0:
factors[2] = factors.get(2, 0) + 1
n = n//2
i = 3
while i < n:
while n % i == 0:
factors[i] = factors.get(i, 0) + 1
n //= i
i += 2
if n > 1:
factors[n] = 1
ut[n] = 1
for i in factors:
ut[n] *= (factors[i] + 1)
return ut[n]
for aa in range(1, a + 1):
for bb in range(1, b + 1):
for cc in range(1, c + 1):
n = aa * bb * cc
if n in dp:
pass
else:
dp[n] = findFactors(n)
res += dp[n]
print(res)
``` | output | 1 | 37,980 | 22 | 75,961 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:
<image>
Find the sum modulo 1073741824 (230).
Input
The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).
Output
Print a single integer — the required sum modulo 1073741824 (230).
Examples
Input
2 2 2
Output
20
Input
5 6 7
Output
1520
Note
For the first example.
* d(1·1·1) = d(1) = 1;
* d(1·1·2) = d(2) = 2;
* d(1·2·1) = d(2) = 2;
* d(1·2·2) = d(4) = 3;
* d(2·1·1) = d(2) = 2;
* d(2·1·2) = d(4) = 3;
* d(2·2·1) = d(4) = 3;
* d(2·2·2) = d(8) = 4.
So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20. | instruction | 0 | 37,981 | 22 | 75,962 |
Tags: implementation, number theory
Correct Solution:
```
#236B
import math
arr = list(map(int, input().split(" ")))
a = arr[0]
b = arr[1]
c = arr[2]
d = dict()
def numdiv(n):
if n in d:
return d[n]
else:
count = 0
for i in range(1, int(math.sqrt(n) + 1)):
if n % i == 0:
count += 2
if int(math.sqrt(n)) * int(math.sqrt(n)) == n:
count -= 1
d[n] = count
return count
answer = 0
for i in range(1, a + 1):
for j in range(1, b + 1):
for k in range(1, c + 1):
answer += numdiv(i * j * k)
print(answer)
``` | output | 1 | 37,981 | 22 | 75,963 |
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