One of my most productive days was throwing away 1,000 lines of code.

— Ken Thompson

Fibonacci addition is an operation on an array $$$X$$$ of integers, parametrized by indices $$$l$$$ and $$$r$$$. Fibonacci addition increases $$$X_l$$$ by $$$F_1$$$, increases $$$X_{l + 1}$$$ by $$$F_2$$$, and so on up to $$$X_r$$$ which is increased by $$$F_{r - l + 1}$$$.

$$$F_i$$$ denotes the $$$i$$$-th Fibonacci number ($$$F_1 = 1$$$, $$$F_2 = 1$$$, $$$F_{i} = F_{i - 1} + F_{i - 2}$$$ for $$$i \gt 2$$$), and all operations are performed modulo $$$MOD$$$.

You are given two arrays $$$A$$$ and $$$B$$$ of the same length. We will ask you to perform several Fibonacci additions on these arrays with different parameters, and after each operation you have to report whether arrays $$$A$$$ and $$$B$$$ are equal modulo $$$MOD$$$.

Input

The first line contains 3 numbers $$$n$$$, $$$q$$$ and $$$MOD$$$ ($$$1 \le n, q \le 3\cdot 10^5, 1 \le MOD \le 10^9+7$$$) — the length of the arrays, the number of operations, and the number modulo which all operations are performed.

The second line contains $$$n$$$ numbers — array $$$A$$$ ($$$0 \le A_i \lt MOD$$$).

The third line also contains $$$n$$$ numbers — array $$$B$$$ ($$$0 \le B_i \lt MOD$$$).

The next $$$q$$$ lines contain character $$$c$$$ and two numbers $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le n$$$) — operation parameters. If $$$c$$$ is "A", Fibonacci addition is to be performed on array $$$A$$$, and if it is is "B", the operation is to be performed on $$$B$$$.

Output

After each operation, print "YES" (without quotes) if the arrays are equal and "NO" otherwise. Letter case does not matter.

Note

Explanation of the test from the condition:

Initially $$$A=[2,2,1]$$$, $$$B=[0,0,0]$$$.
After operation "A 1 3": $$$A=[0,0,0]$$$, $$$B=[0,0,0]$$$ (addition is modulo 3).
After operation "A 1 3": $$$A=[1,1,2]$$$, $$$B=[0,0,0]$$$.
After operation "B 1 1": $$$A=[1,1,2]$$$, $$$B=[1,0,0]$$$.
After operation "B 2 2": $$$A=[1,1,2]$$$, $$$B=[1,1,0]$$$.
After operation "A 3 3": $$$A=[1,1,0]$$$, $$$B=[1,1,0]$$$.

Fibonacci Additions

Examples