You have an initial string S = [s₁, …, s_n].</p>

By definition, S_x,y is a part of string S as follows:

• S_x,y = [s_x, …, s_y], if x ≤ y;
• S_x,y is an empty string, if x > y.

You are given m queries of several types:

1. A question query, given i; j (1 ≤ i ≤ j ≤ n), is the substring [s_i, …, s_j] a palindrome?
2. A modication query which can be of 3 types:
   1. Cut the string into 3 (possibly empty) parts S_1,i-1, S_i,j, S_j+1,n.
      Concatenate the first part with the last one into T= S_1,i-1 S and insert the middle one as follows S’=T S T_k+1,n’ (where n’=n-(j-i+1) respectively), then set S to be equal to S’.
      Note that 1 ≤ i ≤ j ≤ n; 0 ≤ k ≤ n - (j - i + 1).
   2. Reverse the substring S_i,j. Note that 1 ≤ i ≤ j ≤ n.
   3.  Insert a character c at position i, i.e. set S = S_1,i-1 c S_i,n. Note that 1 ≤ i ≤ n+1.
   </li> </ol>

   Note that the value of n will change on modification queries of type (c).

   Write a program that runs the queries above.

   입력 형식

   • The first line contains two space-separated integers n, m.
   • The second line contains n characters representing the initial string.
   • The following m lines contain the description of the m queries.
   • A question query is of the form:
     • Q i j where 1 ≤ i ≤ j ≤ n.
     </ul> </li>
     • A modification query is of the form:
       • M 1 i j k – Modifcation query (a), where i ≤ j.
       • M 2 i j – Modification query (b), where i ≤ j.
       • M 3 i c – Modification query (c), where c is a character.
       </ul> </li> </ul>

       You can assume that the string will contain only lowercase characters of the English alphabet at all times.

       You may assume that the input is valid.

       ## 출력 형식

       For each question query, output a single line of "YES" or "NO" (without quotes).

       ## 예제 입력 6 10 banana Q 2 6 Q 2 5 M 2 2 3 Q 2 5 M 2 5 6 Q 1 6 M 3 7 b Q 1 7 M 1 1 2 4 Q 4 7 ## 예제 출력 YES NO YES NO YES NO ## 힌트

       The modification queries will change the string in the following way:

       • Initially : S = banana
       • Query 1: S = bnaana
       • Query 2: S = bnaaan
       • Query 3: S = bnaaanb
       • Query 4: S = aaanbnb