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 = 10**9 + 7

def pow(num, p):
    global mod
    if p == 1:
        return num 
    ans = pow(num, p//2) 
    if p % 2 == 0:
        return ans * ans % mod
    else:
        return ans * ans * num % mod 

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

if A != 1:
    ans = B
    ans *= ((pow(A, n) - 1) % mod * (pow(A-1, mod - 2) % mod)) % mod
    ans += pow(A, n) * x % mod
    ans %= mod
else:
    ans = x + n * B
    ans %= mod


print(round(ans))
