Limits
1s, 512 MB

We heard you like trees. But this problem has no relation to trees being frozen. :D

You are given a **rooted** tree with `$n$`

nodes. The node with index `$1$`

is the root. Although the tree is not frozen, the tree is colorful. Each of the nodes is colored with a color identified by an integer from `$1$`

to `$m$`

.

You will also be given an array of integers of `$m$`

length. Let's call this array `$A$`

.

There are two types of operations. They are:

**Operation 1:**`$1 ~i ~x$`

.

Set the value of `$A[i]$`

to `$x$`

. It means perform the assignment `$A[i] = x$`

.

**Operation 2:**`$2 ~v ~l ~r$`

.

Consider the **subtree** rooted at node `$v$`

. Lets count occurrences of all the `$m$`

colors in the subtree. We will denote this using `$F_v$`

. It means the `$i^{th}$`

color appears `$F_v [i]$`

times in the subtree rooted at node `$v$`

.

You have to tell if the following statement is true:

Is `$F_v [i] = A[i]$`

for all `$i$`

such that `$l ≤ i ≤ r$`

?

In other words, does the following equation`$F_v [l, l + 1, l + 2, ... r] = A[l, l + 1, l + 2, ... r]$`

hold?

You have to print **"YES"** if the equation is true, otherwise print **"NO"** (without the quotes).

First line will contain three integers `$n, ~m, ~q$`

. They represent the number of nodes, the length of the array `$A$`

and the number of operations respectively.

The next line contains `$n$`

integers, `$c_1, ~c_2, ~c_3 ... ~c_n; ~c_i$`

is the color of the `$i^{th}$`

node.

The next line contains `$m$`

integers, `$a_1, ~a_2, ~a_3 ... ~a_m$`

;

the `$A$`

array.

Next `$n-1$`

lines contain the `$u ~v$`

pairs. They represent the edges in the tree.

Next `$q$`

line will describe the operation.

For type - 1 operation the input is:`$1 ~i ~x$`

.

For type - 2 operation input format is:`$2 ~v ~l ~r$`

.

**Constraints:**`$1 ≤ m ≤ 5 × 10^4$`

.`$1 ≤ n ≤ 5 × 10^4$`

.`$1 ≤ q ≤ 5 × 10^4$`

.`$1 ≤ c_i ≤ m$`

.`$1 ≤ a_i ≤ 10^9$`

.`$1 ≤ u, ~v ≤ n$`

.

For type 1 operation:`$1 ≤ i ≤ m$`

.`$0 ≤ x ≤ 10^9$`

.

For type 2 operation:`$1 ≤ v ≤ n$`

.`$1 ≤ l ≤ r ≤ m$`

.

For each of the type-2 operations, print **"YES"** or **"NO"** without the quotes.

Input | Output |
---|---|

7 4 4 1 1 2 4 4 3 3 2 1 2 3 1 2 2 4 2 5 3 6 3 7 1 3 2 3 2 3 2 3 1 3 1 1 0 2 3 1 3 | YES NO YES |