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 l_i, r_i, k_i. Query l_i, r_i, k_i means that we should add $\text{[math]}$ to each element a[j], where l_i ≤ j ≤ r_i.

Record $\text{[math]}$ 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

The first line contains integers n, m (1 ≤ n, m ≤ 10⁵).

The second line contains n integers a[1], a[2], ..., a[n] (0 ≤ a_i ≤ 10⁹) — the initial array.

Next m lines contain queries in the format l_i, r_i, k_i — to all elements of the segment l_i... r_i add number $\text{[math]}$ (1 ≤ l_i ≤ r_i ≤ n; 0 ≤ k ≤ 100).

Output

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).

Curious Array

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