Arpas family consists of n men. We can show them with a rooted tree with n vertices. Arpa wants to choose k of them for playing football but he shouldn't choose someone and his brother too. In short, there should be no direct siblings, both selected for playing football. Print in how many ways he can choose this set modulo 109+7.
Input Format
The first line contains two integers, n, k (1≤n≤105,0≤k≤100).
The second line contains n−1 integers p2,p3,…,pn (pi<i) -- pi is the index of the parent of i-th person.
Output Format
Print in how many ways he can choose this set modulo 109+7.
Arpa can't choose {3, 5} or {4, 6} but he can choose any other pair.