Fibonacci Additions

Description:

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 $$$A$$$ ($$$0 \le A_i < MOD$$$).

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

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.

Sample Input:

3 5 3
2 2 1
0 0 0
A 1 3
A 1 3
B 1 1
B 2 2
A 3 3

Sample Output:

YES
NO
NO
NO
YES

Sample Input:

5 3 10
2 5 0 3 5
3 5 8 2 5
B 2 3
B 3 4
A 1 2

Sample Output:

NO
NO
YES

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": $$$A=[1,1,0]$$$, $$$B=[1,1,0]$$$.