21064번 - Even Intervals 다국어

문제

You are given an array with $n$ pairwise different values: $A = [a_0, a_1, \dots, a_{n-1}]$. We define the sorted subarray of $A$ starting at $l$ and ending at $r$ as the array that we obtain after sorting $[a_l, a_{l+1}, \dots, a_r]$. For example, if we are given the array $[0,2,14,6,8,10],ドル the sorted subarray starting at 1ドル$ and ending at 4ドル$ would be the array that we would get after sorting $[2,14,6,8],ドル that is, the array $[2,6,8,14]$.

You are given $q$ queries, each one consists of two integers, $l$ and $r$. For each query, print the sum of the values in the even positions of the sorted subarray of $A$ starting at $l$ and ending at $r$. Here, we assume that all arrays are indexed starting from 0ドル$.

For example, consider the array $[0,2,14,6,8,10]$ and the query $(1,4)$. The subarray starting at 1ドル$ and ending at 4ドル$ is just the array $[2,14,6,8]$. Thus, the sorted subarray starting at 1ドル$ and ending at 4ドル$ is the array $[2,6,8,14]$. Now we have to sum the values in even positions, that is, 2ドル+8 = 10$.

Print the answers modulo 10ドル^9 + 7$.

입력

The first line contains two integers $n$ and $q$ (1ドル \leq n \leq 5 \cdot 10^4$; 1ドル \leq q \leq 2 \cdot 10^5$): the number of elements in the array and the number of queries.

The second line contains $n$ integers $a_0, a_1, \dots, a_{n-1}$ (0ドル \leq a_i \leq 10^9$; $a_i$ are pairwise different), the elements of the array.

Finally, each of the next $q$ lines contains two integers $l$ and $r$ (0ドル \leq l \leq r < n$): the starting and ending points of the sorted subarray we are considering.

출력

For each query, print a line with the sum of the elements in even positions of the sorted subarray starting at $l$ and ending at $r$ modulo 10ドル^9 + 7$.

제한

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