Super Power

Compute a^b mod 1337, where the exponent b is a huge number given as a list of its decimal digits (most significant digit first, for example [1, 0] means 10). The list is not empty.

For a = 2 and b = [1, 0] the answer is 1024; for a = 2147483647 and b = [2, 0, 0] it is 1198.

Examples

Example 1

Input:

super_pow(2, [1, 0])

Output:

1024

Example 2

Input:

super_pow(2147483647, [2, 0, 0])

Output:

1198

Constraints

• 1 <= a <= 2**31 - 1
• 1 <= len(b) <= 2000
• Each digit is 0 to 9; b has no leading zero unless b = [0].