Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.

Input

The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.

Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Output

Print the only integer s — the value g(n)(x) modulo 109 + 7.

Examples

Input

3 4 1 1


Output

7


Input

3 4 2 1


Output

25


Input

3 4 3 1


Output

79
A, B, n, x = map(int, input().split())

def fast_exp(A, n, m):
    if n == 0:
        return 1
    if n & 1:
        return A * fast_exp(A, n - 1, m) % m
    return fast_exp(A * A % m, n // 2, m)

def mod(a, m):
    a %= m
    if a < 0:
        a += m
    return a

m = 10**9 + 7

if A == 1:
    print(mod(x + n * B, m))
else:
    ans = B * mod(fast_exp(A, n, m) - 1, m) % m * fast_exp(A - 1, m - 2, m) % m + fast_exp(A, n, m) * x % m
    ans %= m

    print(ans)