You are given an array of n positive integers. Your task is to process q queries where each query can be of two types:

Check if there is a prefix subarray of the given array with a sum equal to a given value s.

Update the value at a specific index of the array.

Write a program to answer the queries efficiently.

Input

The first line contains two integers n and q (1 β€ n, q β€ 100 000), separated by a space, representing the size of the array and the number of queries, respectively.

The second line contains n positive integers, representing the elements of the array, where each element is positive and does not exceed .

The following q lines represent the queries. Each query is represented by a query type (1 or 2) followed by the necessary parameters:

For query type 1: an integer s.

For query type 2: an integer position p and a value x to update at that index.

Output

For each query of type 1, print YES if there exists a prefix subarray with a sum equal to s, otherwise print NO.