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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;
use std::cmp::{max, min};

fn divisors(num: &i32) -> Vec<i32>{
    let mut d = 1i32;
    let mut res = vec![];
    while d * d <= *num{
        if num % d == 0{
            res.push(d);
            if num / d != d {
                res.push(num / d);
            }
        }
        d += 1;
    }
    res
}

fn valid(nums: &Vec<i32>, d: &i32, k:&i32)->bool{
    let mut rems:Vec<i32> = nums.into_iter().map(|x| {x%d}).collect();
    let mut remsum = 0i32;
    for val in &rems{
        remsum += *val;
    }
    rems.sort();
    let mut movecnt = 0i32;
    for i in 0..(rems.len() as i32)-remsum/d{
        movecnt += rems[i as usize];
    }
    movecnt <= *k
}

fn main(){
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n:i32 = iter.next().unwrap().parse().unwrap();
    let k:i32 = iter.next().unwrap().parse().unwrap();

    let mut nums = vec![];
    let mut sum = 0i32;
    for _ in 0..n{
        let a:i32 = iter.next().unwrap().parse().unwrap();
        nums.push(a);
        sum += a;
    }
    let mut divs = divisors(&sum);
    divs.sort();
    divs.reverse();
    for d in divs{
        if valid(&nums, &d, &k){
            println!("{}", d);
            return;
        }
    }
}