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C. Curious Array

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 *l* _{ i}, *r* _{ i}, *k* _{ i}. Query *l* _{ i}, *r* _{ i}, *k* _{ i} means that we should add to each element *a*[*j*], where *l* _{ i} ≤ *j* ≤ *r* _{ i}.

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.

Input

The first line contains integers *n*, *m* (1 ≤ *n*, *m* ≤ 10^{5}).

The second line contains *n* integers *a*[1], *a*[2], ..., *a*[*n*] (0 ≤ *a* _{ i} ≤ 10^{9}) — 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 (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 (10^{9} + 7).

Examples

Input

5 1

0 0 0 0 0

1 5 0

Output

1 1 1 1 1

Input

10 2

1 2 3 4 5 0 0 0 0 0

1 6 1

6 10 2

Output

2 4 6 8 10 7 3 6 10 15

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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