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 = 1000000000+7

if (a == 1):
    print(int((x + n*b)%mod))
    exit()

def fexp(a, b):
    ans = 1
    while b > 0:
        if b%2 == 1:
            ans = (ans * a) % mod
        a = (a * a) % mod
        b = b//2
    return ans

res = ((b * (fexp(a, n) - 1 + mod)) % mod * fexp(a-1, mod-2)) % mod

print(int((res + fexp(a, n) * x) % mod))