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
def mod_pow(base, exp, mod):
    if exp == 0:
        return 1
    if exp == 1:
        return base % mod
    tmp = mod_pow(base, exp // 2, mod)
    tmp = (tmp * tmp) % mod
    if exp % 2 == 1:
        tmp = (tmp * base) % mod
    return tmp

def inv(num, mod):
    return mod_pow(num, mod - 2, mod)
    
a, b, n, x = map(int, input().split())
m = 10 ** 9 + 7
if a == 1:
    ans = (x + ((n * b) % m)) % m
else:
    ans = (mod_pow(a, n, m) * x) % m
    tmp = ((b * inv(a - 1, m)) % m) * ((mod_pow(a, n, m) - 1) % m)
    tmp = tmp % m
    ans = (ans + tmp) % m
print(ans)