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(" "))

xp = pow(a, n % 1000000006, 1000000007)

ans = (xp * x) % 1000000007

if (a == 1):

	ans = ans + n * b

else:

	tmp = (xp - 1) * pow(a - 1, 1000000005, 1000000007) * b

	tmp = tmp % 1000000007

	ans = ans + tmp

ans = ans % 1000000007

print (ans)