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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>
int max(int a, int b){return a>b?a:b;}
int min(int a, int b){return a<b?a:b;}
int gcd(int a, int b){return min(a,b)==0?max(a,b):gcd(min(a,b),max(a,b)%min(a,b));}
long long llmax(long long a, long long b){return a>b?a:b;}
long long llmin(long long a, long long b){return a<b?a:b;}
long long llgcd(long long a, long long b){return min(a,b)==0 ?llmax(a,b):llgcd(llmin(a,b),llmax(a,b)%llmin(a,b));}
int assort(const void *a, const void *b){return *(int*)a-*(int*)b;}
int dessort(const void *a, const void *b){return *(int*)b-*(int*)a;}
int llassort(const void *a, const void *b){return *(long long*)a-*(long long*)b;}
int lldessort(const void *a, const void *b){return *(long long*)b-*(long long*)a;}
int charassort(const void *a, const void *b){return strcmp((char*)a ,(char*)b);}
int chardessort(const void *a, const void *b){return strcmp((char*)b ,(char*)a);}
int ntoi(char c){return c-'0';}
int ltoi(char c){return c-'a';}
int utoi(char c){return c-'A';}
char lowcmp[26]="abcdefghijklmnopqrstuvwxyz";
char upcmp[26]="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
long long mod=1000000007;

int main(void){
    int n,m;
    scanf("%d%d",&n,&m);
    for (int i=m/n; i>=0; i--){
        if (m%i==0){
            printf("%d\n",i);
            break;
        }
    }
	return 0 ;
}