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 power(a, b):
  ret = 1
  while b:
    if b & 1: ret = ret * a % mod
    a = a * a % mod
    b >>= 1
  return ret
def inv(a):
  return power(a, mod - 2)

a, b, n, x = map(int, raw_input().split())

if a == 1:
  ans = x + n * b
else:
  ans = power(a, n) * x % mod + (power(a, n) + mod - 1) % mod * inv(a - 1) % mod * b % mod
print ans % mod