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
def power(m, n)
  count = n
  num = 1

  while count > 0
    num *= m

    num %= 1_000_000_007
    count -= 1
  end

  num
end

m, n = gets.chomp.split(' ').map(&:to_i)

puts power(m, n)