Problem3106--Curious Array

3106: Curious Array

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 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.

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≤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).

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).

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

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