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, mod = 1_000_000_007)
  n = n.to_s(2).split(//).map(&:to_i)
  result = 1
  n.each{|i|
    result *= result
    if i == 1
      result *= m
    end
    result %= mod
  }
  return result, test
end
puts power(gets.split(//).map(&:to_i))