Plasmatic loves playing with playdoughs in his spare time. Currently, he has a collection of ~N~ playdoughs, and the ~i^\text{th}~ playdough weighs ~a_i~ grams for each ~i~ from ~1~ to ~N~. However, he is too busy practicing for IOI. As a result, he doesn't have much time to play with the playdoughs. Instead, he gives you ~Q~ operations that he wants you to do with his collection of playdoughs, and each operation can be one of the two:

1. 1 x: Find all playdoughs that weighs exactly ~x~ grams then split the playdough into ~\lceil \frac{x}{2} \rceil~ and ~\lfloor \frac{x}{2} \rfloor~.

2. 2 y: Find the number of playdoughs that weigh exactly ~y~ grams.

As a good friend of him, you want to print the answers for all of the queries in the form of 2 y. Do not disappoint him!

Constraints

Subtask 1 [15%]

~1 \le N \le 100~

~1 \le Q \le 500~

~1 \le a_i, y \le 100~

~2 \le x \le 100~

Subtask 2 [85%]

~1 \le N \le 10^5~

~1 \le Q \le 5 \cdot 10^5~

~1 \le a_i, y \le 10^5~

~2 \le x \le 10^5~

Note that a 64-bit integer is needed to get full points. In C++, this can be done with long long. In Java, this can be done with long. In Python, the standard int will suffice.

Input Specification

The first line contains two integers ~N~ and ~Q~ separated by a space.

The next line contains ~N~ integers ~a_i~, the weight of each of his playdough originally.

The following ~Q~ lines each contains two space-separated integers, indicating a valid query.

Output Specification

Print the answer to each query of the second type, followed by a newline.

Sample Input

5 4
1 2 3 4 5
1 5
1 4
2 2
2 3

Sample Output

4
2