Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <math.h>
#define max(a,b) ((a)>(b)?(a):(b))
int main(){
  long int n,m,i,ans=1;
  scanf("%ld%ld",&n,&m);
  long int cd[n],cent=sqrtl(m),j=0;
  for(i=1;i<cent;i++){
    if(m%i==0){
      cd[j]=i;
      cd[j+1]=m/i;
      j+=2;
    }
  }
  if(m%cent==0){
    cd[j]=cent;
    j++;
  }
  else cd[j]=0;
  for(i=0;i<=j;i++) if(cd[i]<=m/n)ans=max(ans,cd[i]);
  printf("%ld",ans);
}