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
MOD = 1000000007

def mul_mat_2x2(a, b):
    A = a[0][0]
    B = a[0][1]
    C = a[1][0]
    D = a[1][1]
    X = b[0][0]
    Y = b[0][1]
    G = b[1][0]
    H = b[1][1]
    return [[(B*G + A*X) % MOD, (B*H + A*Y) % MOD], [(D*G + C*X) % MOD, (D*H + C*Y) % MOD]]

def bin_pow_mat_2x2(a, x):
    if(x == 0): 
        return [[1, 0], [0, 1]]
    elif(x == 1):
        return a
    else:
        t = bin_pow_mat_2x2(a, x >> 1)
        ans = mul_mat_2x2(t, t)
        if((x & 1) == 1):
            ans = mul_mat_2x2(ans, a)
        return ans

u, v, n, x = map(int, input().split())
mat = [[u, v], [0, 1]]
s = bin_pow_mat_2x2(mat, n)
f = (s[0][0] * x + s[0][1]) % MOD;
print(f)