YSACODE discuss3

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).

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

2877: Curious Array

Description

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