B. Lipshitz Sequencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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 < 2,   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 .InputThe 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).OutputPrint 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 .ExamplesInput10 41 5 2 9 1 3 4 2 1 72 43 87 101 9Output178223210Input7 65 7 7 4 6 6 21 22 32 61 74 73 5Output202259168NoteIn 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.
Input10 41 5 2 9 1 3 4 2 1 72 43 87 101 9
Output178223210
['data structures', 'math', '*2100']