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())
mod = int(1e9) + 7

def comb(f, g): # f(g(n))
    return (f[0] * g[0] % mod, (f[0] * g[1] + f[1]) % mod)

def exp(fun, n):
    res = (1, 0)
    cp = fun
    for i in range(0, 63):
        if (n >> i) & 1:
            res = comb(cp, res)
        cp = comb(cp, cp)
    return res
    
ans = exp((a, b), n)
print((ans[0] * x + ans[1]) % mod)
