Monk likes math problems very much. His math teacher taught him about sum of digits of a number. He decided to experiment a little with them.

Given a number, he recursively finds the sum of its digits till it becomes a single digit number. He calls this as Digit-Value of a number "

It can be written as :

sumOfDigits(n):
    if n is a single digit number:
        return n
    else:
        x = sum of the digits of n
        return sumOfDigits(x)

After seeing his interest in this concept, his teacher gave him an interesting problem, that uses the above function defined by him. She gave him an array A of N different numbers. Then she asks him Q queries. In each query, he has to form a set of K numbers from the array and find the sum of Digit-Values of those K numbers. This sum is called the value of that set.

The queries are of the following type :
1 K : Monk must output the maximum value of a set of size K, that can be obtained, as described above.

2 K : Monk must output the minimum value of a set of size K, that can be obtained, as described above.

Monk needs your help to complete this task.

Input :

The first line of input contains two space-separated integers N and Q, denoting the number of numbers in the list given by the teacher and the number of queries, respectively. The second line contains N space separated numbers, denoting the array A given by the teacher. The next Q lines contain two space separated integers each, first one to define query type(1 or 2) and second is K, the size of the set to be formed.

Output:

Output contains Q lines. Each of these lines contains an integer that denotes the answer to the \(i^{th}\) query.

Constraints

\(1 \le N \le 10^5\)

\(1 \le Q \le 10^5\)

\(1 \le A_i \le 10^{18}\)

\(1 \le K \le N\)