CF570D.Tree Requests

Roman planted a tree consisting of $n$ vertices. Each vertex contains a lowercase English letter. Vertex $1$ is the root of the tree, each of the $n-1$ remaining vertices has a parent in the tree. Vertex is connected with its parent by an edge. The parent of vertex $i$ is vertex $p_{i}$ , the parent index is always less than the index of the vertex (i.e., p_{i}<i ).

The depth of the vertex is the number of nodes on the path from the root to $v$ along the edges. In particular, the depth of the root is equal to $1$ .

We say that vertex $u$ is in the subtree of vertex $v$ , if we can get from $u$ to $v$ , moving from the vertex to the parent. In particular, vertex $v$ is in its subtree.

Roma gives you $m$ queries, the $i$ -th of which consists of two numbers $v_{i}$ , $h_{i}$ . Let's consider the vertices in the subtree $v_{i}$ located at depth $h_{i}$ . Determine whether you can use the letters written at these vertices to make a string that is a palindrome. The letters that are written in the vertexes, can be rearranged in any order to make a palindrome, but all letters should be used.

The first line contains two integers $n$ , $m$ ( $1<=n,m<=500000$ ) — the number of nodes in the tree and queries, respectively.

The following line contains $n-1$ integers $p_{2},p_{3},...,p_{n}$ — the parents of vertices from the second to the $n$ -th ( 1<=p_{i}<i ).

The next line contains $n$ lowercase English letters, the $i$ -th of these letters is written on vertex $i$ .

Next $m$ lines describe the queries, the $i$ -th line contains two numbers $v_{i}$ , $h_{i}$ ( $1<=v_{i},h_{i}<=n$ ) — the vertex and the depth that appear in the $i$ -th query.

Print $m$ lines. In the $i$ -th line print "Yes" (without the quotes), if in the $i$ -th query you can make a palindrome from the letters written on the vertices, otherwise print "No" (without the quotes).

String $s$ is a palindrome if reads the same from left to right and from right to left. In particular, an empty string is a palindrome.

Clarification for the sample test.

In the first query there exists only a vertex 1 satisfying all the conditions, we can form a palindrome "z".

In the second query vertices 5 and 6 satisfy condititions, they contain letters "с" and "d" respectively. It is impossible to form a palindrome of them.

In the third query there exist no vertices at depth 1 and in subtree of 4. We may form an empty palindrome.

In the fourth query there exist no vertices in subtree of 6 at depth 1. We may form an empty palindrome.

In the fifth query there vertices 2, 3 and 4 satisfying all conditions above, they contain letters "a", "c" and "c". We may form a palindrome "cac".