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 pow(a, n):
	if (n == 0):
		return 1
	if (n % 2 == 0):
		return (pow(a, n//2) ** 2) % (1000000007)
	else:
		return (a * pow(a, n//2) ** 2) % (1000000007)



M = 1000000007
a, b, n, x = map(int, input().split())
arr = [0] * 64
arr[0] = b;
for i in range(1, 64):
	arr[i] = ((pow(a, 2**(i-1)) * arr[i-1]) % M + arr[i-1]) % M;
ans = (pow(a, n) * x) % M;
pos = 0;
for i in range(63, -1, -1):
	if (2**i <= n) :
		ans += (pow(a, pos) * arr[i]) % M;
		ans %= M;
		n -= 2**i;
		pos += 2**i;
print(ans%M)