def gcd(a, b):
    while a:
        a, b = b%a, a
    return b

def is_prime(n):
    if n == 2:
        return 1
    if n == 1 or n%2 == 0:
        return 0

    m = n - 1
    lsb = m & -m
    s = lsb.bit_length()-1
    d = m // lsb

    test_numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]

    for a in test_numbers:
        if a == n:
            continue
        x = pow(a,d,n)
        r = 0
        if x == 1:
            continue
        while x != m:
            x = pow(x,2,n)
            r += 1
            if x == 1 or r == s:
                return 0
    return 1

def find_prime_factor(n):
    if n%2 == 0:
        return 2

    m = int(n**0.125)+1

    for c in range(1,n):
        f = lambda a: (pow(a,2,n)+c)%n
        y = 0
        g = q = r = 1
        k = 0
        while g == 1:
            x = y
            while k < 3*r//4:
                y = f(y)
                k += 1
            while k < r and g == 1:
                ys = y
                for _ in range(min(m, r-k)):
                    y = f(y)
                    q = q*abs(x-y)%n
                g = gcd(q,n)
                k += m
            k = r
            r *= 2
        if g == n:
            g = 1
            y = ys
            while g == 1:
                y = f(y)
                g = gcd(abs(x-y),n)
        if g == n:
            continue
        if is_prime(g):
            return g
        elif is_prime(n//g):
            return n//g
        else:
            return find_prime_factor(g)

def factorize(n):
    res = []
    while not is_prime(n) and n > 1:  # nが合成数である間nの素因数の探索を繰り返す
        p = find_prime_factor(n)
        s = 0
        while n%p == 0:  # nが素因数pで割れる間割り続け、出力に追加
            n //= p
            s += 1
        res.append((p, s))
    if n > 1:  # n>1であればnは素数なので出力に追加
        res.append((n, 1))
    return res

def divisor(n):
    ans = [1]
    pf = factorize(n)
    for p, c in pf:
        L = len(ans)
        for i in range(L):
            v = 1
            for _ in range(c):
                v *= p
                ans.append(ans[i]*v)
    return sorted(ans)

N, K = map(int, input().split())
A = list(map(int, input().split()))

ans = 1
for op in range(-K, K+1):
    div = divisor(A[0]+op)
    for d in div[::-1]:
        r = K-abs(op)
        for i in range(1, N):
            left = A[i]%d
            right = d-left
            r -= min(left, right)
            if r < 0:
                break
        else:
            ans = max(ans, d)
            break

print(ans)