B'Mr. Chanek opened a letter from his fellow, who is currently studying at Singanesia. Here is what it says. Define an array b ( 0 <= q b_i < k ) with n integers. While there exists a pair (i, j) such that b_i ne b_j , do the following operation: Denote f(b) as the expected number of operations done to b until all elements of b are equal. You are given two integers n and k , and an array a ( -1 <= q a_i < k ) of n integers. For every index i with a_i = -1 , replace a_i with a random number j satisfying 0 <= q j < k . Let c be the number of occurrences of -1 in a . There are k^c possibilites of a after the replacement, each with equal probability of being the final array. Find the expected value of f(a) modulo 10^9 + 7 . Formally, let M = 10^9 + 7 . It can be shown that the answer can be expressed as an irreducible fraction frac{p}{q} , where p and q are integers and q not equiv 0 pmod{M} . Output the integer equal to p cdot q^{-1} bmod M . In other words, output such an integer x that 0 <= x < M and x cdot q equiv p pmod{M} . After reading the letter, Mr. Chanek gave the task to you. Solve it for the sake of their friendship! The first line contains two integers n and k ( 2 <= q n <= q 10^5 , 2 <= q k <= q 10^9 ). The second line contains n integers a_1, a_2, ldots, a_n ( -1 <= q a_i < k ). Output an integer denoting the expected value of f(a) modulo 10^9 + 7 . '...