Missing Coin Sum Queries

• Time limit: 1.00 s
• Memory limit: 512 MB

You have $n$ coins with positive integer values. The coins are numbered $1,2,\dots,n$.

Your task is to process $q$ queries of the form: "if you can use coins $a \dots b$, what is the smallest sum you cannot produce?"

Input

The first input line has two integers $n$ and $q$: the number of coins and queries.

The second line has $n$ integers $x_1,x_2,\dots,x_n$: the value of each coin.

Finally, there are $q$ lines that describe the queries. Each line has two values $a$ and $b$: you can use coins $a \dots b$.

Output

Print the answer for each query.

Constraints

• $1 \le n, q \le 2 \cdot 10^5$
  
• $1 \le x_i \le 10^9$
  
• $1 \le a \le b \le n$
  

Example

Input:
5 3
2 9 1 2 7
2 4
4 4
1 5

Output:
4
1
6

Explanation: First you can use coins $[9,1,2]$, then coins $[2]$ and finally coins $[2,9,1,2,7]$.