A function is called Lipschitz continuous if there is a real constant K such that the inequality f(x) - f(y) ≤ K·x - y holds for all . We'll deal with a more... discrete version of this term. For an array , we define it's Lipschitz constant as follows: if n , if n ≥ 2, over all 1 ≤ i j ≤ n In other words, is the smallest non-negative integer such that h[i] - h[j] ≤ L·i - j holds for all 1 ≤ i, j ≤ n . You are given an array of size n and q queries of the form [l, r]. For each query, consider the subarray ; determine the sum of Lipschitz constants of all subarrays of .
输入描述:
The first line of the input contains two space-separated integers n and q (2 ≤ n ≤ 100 000 and 1 ≤ q ≤ 100) — the number of elements in array and the number of queries respectively.The second line contains n space-separated integers ().The following q lines describe queries. The i-th of those lines contains two space-separated integers li and ri (1 ≤ li ri ≤ n).
输出描述:
Print the answers to all queries in the order in which they are given in the input. For the i-th query, print one line containing a single integer — the sum of Lipschitz constants of all subarrays of .
示例1
输入
10 4
1 5 2 9 1 3 4 2 1 7
2 4
3 8
7 10
1 9
7 6
5 7 7 4 6 6 2
1 2
2 3
2 6
1 7
4 7
3 5
输出
17
82
23
210
2
0
22
59
16
8
备注:
In the first query of the first sample, the Lipschitz constants of subarrays of with length at least 2 are:The answer to the query is their sum.
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