Sequence Modulo Range Update and Subarray Equality

You are given three positive integers \(n\), \(k\) and \(q\), and a sequence \(a\) of length \(n\). You need to process \(q\) operations or queries on the sequence. There are two types of operations:

• Update: 1 l r c — For every index \(i\) from \(l\) to \(r\) (inclusive), update \(a_i = (a_i+c) \bmod k\).
• Query: 2 l_1 r_1 l_2 r_2 — Check whether the two subarrays \(a[l_1\cdots r_1]\) and \(a[l_2\cdots r_2]\) are equal. Print Yes if they are equal, and No otherwise.

The operations are given in the order of input. Process each operation accordingly.

inputFormat

The first line contains three integers \(n\), \(k\) and \(q\). The second line contains \(n\) integers representing the sequence \(a_1, a_2, \ldots, a_n\). Each of the next \(q\) lines describes an operation in one of the two formats:

• 1 l r c — update operation (add \(c\) modulo \(k\) to each element from index \(l\) to \(r\)).
• 2 l1 r1 l2 r2 — query operation (check if subarray \(a[l1..r1]\) equals subarray \(a[l2..r2]\)).

outputFormat

For each query operation (type 2), output a single line containing either Yes or No indicating whether the two specified subarrays are equal.

sample

5 10 5
1 2 3 4 5
1 1 3 2
2 1 2 4 5
1 2 5 3
2 1 3 3 5
2 3 5 3 5

No
No
Yes