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
line = raw_input()

A, B, n, x = line.split()
mod = 1000000007

def matmult(a, b):
	return [
		a[0]%mod*b[0]%mod+a[1]%mod*b[2]%mod, 
		a[0]%mod*b[1]%mod+a[1]%mod*b[3]%mod,
		a[2]%mod*b[0]%mod+a[3]%mod*b[2]%mod,
		a[2]%mod*b[1]%mod+a[3]%mod*b[3]%mod
		]

a0 = [int(A), 1, 0, 1]

def modpow(a, b):
	if b == 1:
		return a0
	elif b & 1 == 1:
		return matmult(a0, modpow(a,b-1))
	else:
		x = modpow(a, b/2)
		return matmult(x, x)
		
an = modpow(a0, int(n))
print (an[0]*int(x)+an[1]*int(B))%mod