Curious Array

给出$n$个数，有$m$个操作. 每个操作是将$[L,R]$之间的数加上$C(j-L+k,k)$，$L<=j<=R$. 最后输出这$n$个数的值。

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  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.

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 $ ).

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) $ .

5 1
0 0 0 0 0
1 5 0

1 1 1 1 1

10 2
1 2 3 4 5 0 0 0 0 0
1 6 1
6 10 2

2 4 6 8 10 7 3 6 10 15