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: Accepted)

'use strict'

class Main {
  solve() {
    const nm = input.nextIntArr();
    return _.max(Prime.getDivisors(nm[1]).filter(e => e <= nm[1]/nm[0]));
  }
}

class Prime {
  /* 初期化と素数テーブル生成 */
  constructor(n) {
    if (n == null) { n = 100000; }
    const primeTable = [...((new Array(n)).keys())];
    primeTable[0] = false;
    primeTable[1] = false;
    let max = Math.sqrt(n);
    for(let i = 2;i <= max;++i) {
      if (primeTable[i] !== i) continue;
      for (let j = i * i; j < n; j += i) {
        if (primeTable[j] !== j) continue;
        primeTable[j] = i;
      }
    }
    this.size = n;
    this.primeTable = primeTable;
    this.primeList = primeTable.filter((e,i) => e === i);
  }

  /* テーブルに生成した素数の2乗までの素数判定 */
  isPrime(n) {
    if (n < this.size) return this.primeTable[n] === n;
    let max = Math.sqrt(n);
    for (let i = 0; this.primeList[i] <= max; ++i) {
      if (n % this.primeList[i] === 0) return false;
    }
    return true;
  }

  /* 最小の素因数 */
  getMinimumFactor(n) {
    if (n < this.size) return this.primeTable[n];
    let max = Math.sqrt(n);
    for (let i = 0; this.primeList[i] <= max; ++i) {
      if (n % this.primeList[i] === 0) return this.primeList[i];
    }
    return n;
  }

  /* 素因数の取得
   * 上限: テーブルサイズの二乗*/
  getFactor(n) {
    const ret = [];
    let k = n;
    while(!this.isPrime(k)) {
      const p = this.getMinimumFactor(k)
      ret.push(p);
      k /= p;
    }
    ret.push(k);
    return ret;
  }

  /* 素因数テーブル
   * 上限: テーブルサイズ*/
  getFactorTable(n) {
    const factor = this.getFactor(n);
    const maxFactor = factor[factor.length - 1];
    const ret = [];
    for (let i = 0;this.primeList[i] <= maxFactor; ++i) {
      ret[this.primeList[i]] = 0;
    }
    for (const e of factor) { ++ret[e]; }
    return ret;
  }
  
  /* 約数の個数 */
  getDivisorCount(n) {
    const factor = this.getFactor(n);
    let count = 1;
    let prev = factor[0];
    let factorCount = [];
    for (let i = 1; i < factor.length; ++i) {
      if (factor[i] != prev) {
        factorCount.push(count);
        count = 1;
      }
      else {
        ++count;
      }
      prev = factor[i];
    }
    factorCount.push(count);
    return factorCount.reduce((a,b)=>a * (b+1),1);
  }

  /* 約数の一覧の取得(未ソート) O(√n)*/
  static getDivisors(n) {
    let max = Math.sqrt(n);
    let ret = [];
    if (n % max === 0) {ret.push(max);}
    for(let i = 0; i < max; ++i) {
      if (n % i == 0) {
        ret.push(i);
        ret.push(n / i);
      }
    }
    return ret;
  }
}

const prime = new Prime(1000);
class Underscore {
  sum(arr) { return arr.reduce((a,b)=>a+b); }
  min(arr, func) { if (func == null) {func = (a,b) => a - b} return arr.reduce((a,b) => func(a,b) < 0 ? a : b); }
  max(arr, func) { if (func == null) {func = (a,b) => a - b} return arr.reduce((a,b) => func(a,b) > 0 ? a : b); }
  sort(arr, func) { if (func == null) {func = (a,b) => a - b} return arr.sort(func) }
  range(start, stop, step) {
	if (stop == null) {
	  stop = start || 0;
	  start = 0;
	}
	if (!step) {
	  step = stop < start ? -1 : 1;
	}
	const length = Math.max(Math.ceil((stop - start) / step), 0);
	const range = Array(length);

	for (var idx = 0; idx < length; idx++, start += step) {
	  range[idx] = start;
	}
	return range;
  }

  first (array, n) {
    if (array == null || array.length < 1) return n == null ? void 0 : [];
    if (n == null) return array[0];
    return this.initial(array, array.length - n);
  };

  initial (array, n) { return array.slice.call(array, 0, Math.max(0, array.length - (n == null ? 1 : n))); }

  tail(array, n) { return array.slice.call(array, n == null ? 1 : n); }

  last (array, n) { 
    if (n == null) return array[array.length - 1];
    return this.tail(array, Math.max(0, array.length - n)); 
  }

  /* 累積和 */
  sumArray (arr) { return this.tail(arr.reduce(((a,b,i) => {a.push(b + a[i]); return a}), [0])); }

  binarySearch (array, key, iteratee) {
	const itr = (obj) => (typeof obj === 'object') ? obj[iteratee] : obj;
	const value = itr(obj);
	let low = 0, high = array.length;
	while (low < high) {
	  let mid = Math.floor((low + high) / 2);
	  if (itr(array[mid]) < value) low = mid + 1; else high = mid;
	}
	return low;
  };
}
const _ = new Underscore();

class Input {
  constructor() {
	this.cursor = 0;
	this.inputAll();
  }

  inputAll() {
	this.data = (require("fs").readFileSync("/dev/stdin", "utf8")).split('\n');
	return this.data;
  }

  /* 1行 or 複数行文字列 */
  nextLine(n) {
	if (n) {
	  const ret = this.data.slice(this.cursor, this.cursor + n);
	  this.cursor += n;
	  return ret;
	}
	return this.data[this.cursor++];
  }
  /* 1整数 */
  nextInt() { return parseInt(this.nextLine()); } 
  /* 一行文字配列 */
  nextStrArr() { return this.nextLine().split(' '); } 
  /* 一行整数配列 */
  nextIntArr() { return this.nextStrArr().map((e) => parseInt(e)); }
  /* 一行浮動小数点配列 */
  nextFloatArr() { return this.nextStrArr().map((e) => parseFloat(e)); }
  /* 複数行整数配列 */
  nextIntLine(n) { return this.nextLine(n).map((e) => parseInt(e)) }
  /* 複数行浮動小数点配列 */
  nextFloatLine(n) { return this.nextLine(n).map((e) => parseFloat(e)) }
  /* 複数行文字列二次元配列 */
  nextStrRange(n) { return this.nextLine(n).map((line) => line.split(' ')); }
  /* 複数行整数二次元配列 */
  nextIntRange(n) {
	return this.nextLine(n).map((line) => line.split(' ').map((e) => parseInt(e)));
  }
  /* 複数行浮動小数点数二次元配列 */
  nextFloatRange(n) {
	return this.nextLine(n).map((line) => line.split(' ').map((e) => parseFloat(e)));
  }
} 
const input = new Input();

const Out = (output) => {
  let ret;
  if (output == null) return;
  if (output === true) { ret = 'Yes'; }
  else if (output === false) { ret = 'No'; }
  else { ret = output; }
  console.log(ret);
}

Out(new Main().solve());