Description:
You'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 $${ \binom { j - l _ { i } + k _ { i } } { k _ { i } } }$$ to each element a[j], where li ≤ j ≤ ri.
Record $${ \frac { y } { x } }$$ 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.
Input Format:
The 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 $${ \binom { j - l _ { i } + k _ { i } } { k _ { i } } }$$ (1 ≤ li ≤ ri ≤ n; 0 ≤ k ≤ 100).
Output Format:
Print 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).
Note:
None