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 = int(1e9) + 7

def binpow(a, b):
    a %= MOD
    res = 1
    while b > 0:
        if b % 2 != 0:
            res = (res * a) % MOD
        a = (a * a) % MOD
        b >>= 1
    
    return res

def divide(a, b):
    return a * binpow(b, MOD - 2) % MOD


inp = input().strip().split(" ")
a = int(inp[0]); b = int(inp[1]); n = int(inp[2]); x = int(inp[3])


res = (binpow(a, n) * x) % MOD

if a == 1:
    res = (res + b * n % MOD) % MOD

else:
    res = (res + b * divide((binpow(a, n) - 1) % MOD , (a-1) % MOD )) % MOD

print(res)