Cities

문제

In a far away kingdom, there are $NN$ cities numbered between $00$ and $N-1N\; -\; 1$. The cities are connected by $N-1N\; -\; 1$ two-way roads. Each road has the same length, and connects exactly two cities, such that there is a unique path between any pair of cities.

For any two cities $AA$ and $BB$, denote by $L(A,B)L(A,\; B)$ the number of roads of this unique path between cities $AA$ and $BB$. Given an integer $KK$, for how many pairs of cities $A,BA,\; B$ is $L(A,B)=KL(A,\; B)\; =\; K$?

입력

The sample judge reads input in the following format:

• line $11$: N K
• line $22$: F[0] F[1] .. F[N - 2]
• line $33$: T[0] T[1] .. T[N - 2]

출력

The sample judge will write a single line with the return value of paths(N, K, F, T).