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: Time Limit Exceeded)

#include <malloc.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>

//ABC112D
int compare_int(const void *a, const void *b) { //sort
  return *(int*) a-*(int*) b;
}

int main(void) {
  int n, m, k=0, i, cou=0, tho=1000;
  int memo[tho];
  scanf(" %d %d", &n, &m);
  int sqm=sqrt(m);
  //printf("sqm=%d\n", sqm);

  for(i=0; i<tho; i++)
    memo[i]=1;
  for(i=sqm; i>=1; i++){
    if(m%i==0) memo[k++ ]=i, memo[k++ ]=m/i;
  }
  qsort(memo, k, sizeof(int), compare_int); //sort

  for(i=0; i<k; i++){
    if(memo[i]>=n){
      printf("%d", m/memo[i]);
      return 0;
    }
  }
  return 0;
}