Problem:
Score : 500 points

Problem Statement

We have a sequence of N integers: A_1, A_2, \cdots, A_N.

You can perform the following operation between 0 and K times (inclusive):

Choose two integers i and j such that i \neq j, each between 1 and N (inclusive). Add 1 to A_i and -1 to A_j, possibly producing a negative element.

Compute the maximum possible positive integer that divides every element of A after the operations. Here a positive integer x divides an integer y if and only if there exists an integer z such that y = xz.

Constraints

2 \leq N \leq 500

1 \leq A_i \leq 10^6

0 \leq K \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_{N-1} A_{N}

Output

Print the maximum possible positive integer that divides every element of A after the operations.

Sample Input 1

2 3
8 20

Sample Output 1

7

7 will divide every element of A if, for example, we perform the following operation:

Choose i = 2, j = 1. A becomes (7, 21).

We cannot reach the situation where 8 or greater integer divides every element of A.

Sample Input 2

2 10
3 5

Sample Output 2

8

Consider performing the following five operations:

Choose i = 2, j = 1. A becomes (2, 6).

Choose i = 2, j = 1. A becomes (1, 7).

Choose i = 2, j = 1. A becomes (0, 8).

Choose i = 2, j = 1. A becomes (-1, 9).

Choose i = 1, j = 2. A becomes (0, 8).

Then, 0 = 8 \times 0 and 8 = 8 \times 1, so 8 divides every element of A. We cannot reach the situation where 9 or greater integer divides every element of A.

Sample Input 3

4 5
10 1 2 22

Sample Output 3

7

Sample Input 4

8 7
1 7 5 6 8 2 6 5

Sample Output 4

5

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var sc *bufio.Scanner

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc = bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n, k := nextInt(), nextInt()

	aArray := make([]int, n)
	aSum := 0
	for i := range aArray {
		aArray[i] = nextInt()
		aSum += aArray[i]
	}

	var div []int
	for i := 1; i*i <= aSum; i++ {
		if aSum%i == 0 {
			div = append(div, i)
			if i != aSum/i {
				div = append(div, aSum/i)
			}
		}
	}
	sort.Sort(sort.Reverse(sort.IntSlice(div)))

	for _, d := range div {
		mod := make([]int, n)
		for i, a := range aArray {
			mod[i] = a % d
		}
		sort.Sort(sort.IntSlice(mod))
		modSum := 0
		for _, m := range mod {
			modSum += m
		}
		if modSum == 0 {
			fmt.Println(d)
			return
		}
		modDiff := 0
		for i := n - 1; modSum > modDiff; i-- {
			modSum -= mod[i]
			modDiff += d - mod[i]
		}
		if modSum == modDiff && modSum <= k {
			fmt.Println(d)
			return
		}
	}
}