Little Mirko spends his free time painting. For this hobby, he likes to use brushes and a pallet containing K colors overall. His friend Slavko decided to use Mirko’s talent and gave him his new coloring book for Mirko to color. The coloring book contains N images numbered 1, 2, …, N.
Mirko has decided to paint each image in exactly one color of the possible K colors from his pallet.However, he really likes colorful things. He chose N numbers fi and decided to paint the image numbered i differently than the images numbered fi, except when fi = i. If fi = i, that means he can paint the image numbered fi whichever color he likes, as long as all other conditions have been met.
Mirko wants to know the number of possible ways to color Slavko’s coloring book and he desperately needs your help! Calculate the number of possible ways to color the book. Given the fact that the output can be very large, print the answer modulo 1000000007.
The first line of input contains positive integers N, K.
Following line contains N numbers fi, the number stated in the text.
1 ≤ N ≤ 1000000
1 ≤ K ≤ 1000000
1 ≤ fi ≤ N
Time limit = 1 sec
The first and only line must contain the number of possible ways to color Slavko's book.
Sample Input 1:
Sample Output 1:
Sample Input 2:
2 3 1
Sample Output 2:
For Sample Input 1:
Mirko has three colors and decided that the image numbered 2 mustn't be of the same color as the image numbered 1. The possible colorings are (1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2), where the first number in the brackets represents the color of the first image and the second number the color of the second image.