You are given an array A containing N integers where every integer is represented as a 23-bit binary string. You are also given the following function:

\(F(x,y) = Length\ of\ Longest\ Common\ Suffix\ of\ x\ and\ y\)

Write a program to resolve Q queries of the following types:

\(1\ x\ y\ \) : Update \(A[x] = y\)
\(2\ L\ R\ x\) : Print sum of \(F(A[i], x)\) for \(L \le i \le R\)

Input format

First line: Two space-separated integers N and Q
Second line: N space-separated integers (denoting the array A)
Next Q lines: Query of either type

Output format

For each query of the second type, print the required sum.

Constraints

\(1 \le N,Q \le 10^{5}\)
\(1 \le L \le R \le N\)
\(1 \le A[i], x \le 8388607\)