Power

For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.

Constraints

• 1 ≤ m ≤ 100
• 1 ≤ n ≤ 109

Input

m n

Two integers m and n are given in a line.

Output

Print mn (mod 1,000,000,007) in a line.

Examples

Input

2 3

Output

8

Input

5 8

Output

390625

inputFormat

Input

m n

Two integers m and n are given in a line.

outputFormat

Output

Print mn (mod 1,000,000,007) in a line.

Examples

Input

2 3

Output

8

Input

5 8

Output

390625

样例

2 3

8