Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

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(2).readFileSync("/dev/stdin","UTF-8"))},function(r,e){function t(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")}()}r.exports=function(r){var e=t(r.split("\n")[0].split(" ").map(function(r){return Number(r)}),2),n=e[0],o=e[1],u={1:o};u[o]=1;for(var i=Math.sqrt(o),f=2;f<i;f++)if(o%f==0){u[f]=0;for(var l=o;l>0&&l%f==0;)l/=f,u[f]+=1}var a=1;for(var c in u)u[c]>=n&&Number(c)>a&&(a=Number(c));console.log(a)}},function(r,e){r.exports=require("fs")}]);