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

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 $[2,9,1,2,7]$.