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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

module.exports=function(r){var e={};function t(n){if(e[n])return e[n].exports;var o=e[n]={i:n,l:!1,exports:{}};return r[n].call(o.exports,o,o.exports,t),o.l=!0,o.exports}return t.m=r,t.c=e,t.d=function(r,e,n){t.o(r,e)||Object.defineProperty(r,e,{enumerable:!0,get:n})},t.r=function(r){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(r,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(r,"__esModule",{value:!0})},t.t=function(r,e){if(1&e&&(r=t(r)),8&e)return r;if(4&e&&"object"==typeof r&&r&&r.__esModule)return r;var n=Object.create(null);if(t.r(n),Object.defineProperty(n,"default",{enumerable:!0,value:r}),2&e&&"string"!=typeof r)for(var o in r)t.d(n,o,function(e){return r[e]}.bind(null,o));return n},t.n=function(r){var e=r&&r.__esModule?function(){return r.default}:function(){return r};return t.d(e,"a",e),e},t.o=function(r,e){return Object.prototype.hasOwnProperty.call(r,e)},t.p="",t(t.s=0)}([function(r,e,t){t(1)(t(3).readFileSync("/dev/stdin","UTF-8").split("\n"))},function(r,e,t){function n(r,e){return function(r){if(Array.isArray(r))return r}(r)||function(r,e){var t=[],n=!0,o=!1,u=void 0;try{for(var i,f=r[Symbol.iterator]();!(n=(i=f.next()).done)&&(t.push(i.value),!e||t.length!==e);n=!0);}catch(r){o=!0,u=r}finally{try{n||null==f.return||f.return()}finally{if(o)throw u}}return t}(r,e)||function(){throw new TypeError("Invalid attempt to destructure non-iterable instance")}()}var o=t(2);r.exports=function(r){var e=n(r[0].split(" ").map(function(r){return Number(r)}),2),t=e[0],u=e[1];if(u%t!=0){var i=o(u),f=1;for(var a in i){var l=i[a];if(!(Math.pow(a,l)<t)){for(;f<t&&l>0;)f*=a,l--;if(f>=t)break}}var c=u/f;console.log(c)}else console.log(u/t)}},function(r,e){r.exports=function(r){for(var e={},t=r,n=Math.ceil(Math.sqrt(r)),o=2;o<n+1;o++){for(var u=0;t%o==0;)t/=o,u++;if(u>0&&(e[o]=u),t<=0)break}return t>1&&(e[t]=1),e}},function(r,e){r.exports=require("fs")}]);