C. Curious Arraytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou've got an array consisting of n integers: a[1], a[2], ..., a[n]. Moreover, there are m queries, each query can be described by three integers li, ri, ki. Query li, ri, ki means that we should add  to each element a[j], where li ≤ j ≤ ri.Record  means the binomial coefficient, or the number of combinations from y elements into groups of x elements.You need to fulfil consecutively all queries and then print the final array.InputThe first line contains integers n, m (1 ≤ n, m ≤ 105).The second line contains n integers a[1], a[2], ..., a[n] (0 ≤ ai ≤ 109) — the initial array.Next m lines contain queries in the format li, ri, ki — to all elements of the segment li... ri add number  (1 ≤ li ≤ ri ≤ n; 0 ≤ k ≤ 100).OutputPrint n integers: the i-th number is the value of element a[i] after all the queries. As the values can be rather large, print them modulo 1000000007 (109 + 7).ExamplesInput5 10 0 0 0 01 5 0Output1 1 1 1 1Input10 21 2 3 4 5 0 0 0 0 01 6 16 10 2Output2 4 6 8 10 7 3 6 10 15
Input5 10 0 0 0 01 5 0
Output1 1 1 1 1
['brute force', 'combinatorics', 'implementation', 'math', '*2500']