MOD = 1000000007


def pow_mod(a, k, p):
    t = []
    pow_val = 1  # 2的次幂数, 初始是2^0 = 1
    a_pow = a % p  # a^(2 ^ i)的数值, 初始是a^(2^0) = a
    while pow_val <= k:
        t.append(a_pow)
        a_pow = (a_pow * a_pow) % p
        pow_val <<= 1

    ans = 1
    for i in range(len(t)):
        if k & 1:
            ans = (ans * t[i]) % p
        k >>= 1
    return ans


# 提前把20以内阶乘的逆元都算好
_vals = [1] * 21
k = 1
for ii in range(1, 21):
    k = (k * ii) % MOD
    _vals[ii] = pow_mod(k, MOD-2, MOD)

def C(a, b, p):
    b = min(b, a - b)

    i, j = 1, a
    val, _val = 1, _vals[b]
    while i <= b:
        val = (val * j) % p
        i, j = i + 1, j - 1


    # 乘法逆元做除法
    val = (val * _val) % p
    return val


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

total_method_num = C(M + N - 1, N - 1, MOD)

invalid_method_num = 0
for stat in range(1, 1 << N):
    # print(bin(stat))

    one_cnt = 0
    S = 0
    for i in range(N):
        if stat & (1 << i):
            one_cnt += 1
            S += A[i] + 1

    if S <= M:
        bad_method_num = C(M + N - S - 1, N - 1, MOD)
        if one_cnt & 1:
            total_method_num -= bad_method_num
            total_method_num %= MOD
        else:
            total_method_num += bad_method_num
            total_method_num %= MOD

print(total_method_num)