The problem statement is simple.

You are given an array A of N integers. You have to answer Q queries of three types.

1 L R : Determine if the subarray [ A_L , A_L+1 , A_L+2 , ..... A_R ] is special or not.
2 L R X Y : Multiply all the elements of the subarray [ A_L , A_L+1 , A_L+2 , ..... A_R ] by X^Y.
3 L R X : Reset all the elements of the subarray [ A_L , A_L+1 , A_L+2 , ..... A_R ] to value X.

Let \(val=\prod_{i=L}^R A_i\) = Product of the subarray [ A_L , A_L+1 , A_L+2 , ..... A_R ]

A subarray is special if \(\sqrt[K]{val}\) is a integer . In other words the K^th root of product of the subarray should be a integer.

Input Format

First line contains three integers N K Q.

Next line contains N integers A₁ , A₂ , A₃ , ..... A_N .

Next Q lines contains one of the three types of queries.

Constraints

For each query of type 1 , print Yes if the subarray is special else No