Yash And Trees

题意翻译

一棵树两种操作，第一种是某一节点子树所有值+v， 第二种问子树中节点模m出现了多少种m以内的质数。

题目描述

Yash loves playing with trees and gets especially excited when they have something to do with prime numbers. On his 20th birthday he was granted with a rooted tree of $ n $ nodes to answer queries on. Hearing of prime numbers on trees, Yash gets too intoxicated with excitement and asks you to help out and answer queries on trees for him. Tree is rooted at node $ 1 $ . Each node $ i $ has some value $ a_{i} $ associated with it. Also, integer $ m $ is given. There are queries of two types: 1. for given node $ v $ and integer value $ x $ , increase all $ a_{i} $ in the subtree of node $ v $ by value $ x $ 2. for given node $ v $ , find the number of prime numbers $ p $ less than $ m $ , for which there exists a node $ u $ in the subtree of $ v $ and a non-negative integer value $ k $ , such that $ a_{u}=p+m·k $ .

输入输出格式

输入格式

The first of the input contains two integers $ n $ and $ m $ ( $ 1<=n<=100000,1<=m<=1000 $ ) — the number of nodes in the tree and value $ m $ from the problem statement, respectively. The second line consists of $ n $ integers $ a_{i} $ ( $ 0<=a_{i}<=10^{9} $ ) — initial values of the nodes. Then follow $ n-1 $ lines that describe the tree. Each of them contains two integers $ u_{i} $ and $ v_{i} $ ( $ 1<=u_{i},v_{i}<=n $ ) — indices of nodes connected by the $ i $ -th edge. Next line contains a single integer $ q $ ( $ 1<=q<=100000 $ ) — the number of queries to proceed. Each of the last $ q $ lines is either 1 v x or 2 v ( $ 1<=v<=n,0<=x<=10^{9} $ ), giving the query of the first or the second type, respectively. It's guaranteed that there will be at least one query of the second type.

输出格式

For each of the queries of the second type print the number of suitable prime numbers.

输入输出样例

输入样例 #1

8 20
3 7 9 8 4 11 7 3
1 2
1 3
3 4
4 5
4 6
4 7
5 8
4
2 1
1 1 1
2 5
2 4

输出样例 #1

3
1
1

输入样例 #2

5 10
8 7 5 1 0
1 2
2 3
1 5
2 4
3
1 1 0
1 1 2
2 2

输出样例 #2

2