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Let's consider a rectangular table R consisting of N rows and M columns. Rows are enumerated from 1 to N from top to bottom. Columns are enumerated from 1 to M from left to right. Each element of R is a non-negative integer. R is called steady if the sum of elements in the ith row is not less then the sum of elements in the (i-1)th row for each i where 2 ≤ i ≤ N and the sum of elements in the Nth row is less than or equal to M. Your task is to find the number of different steady tables of size N x M modulo 1 000 000 000.
The first line of input contains a single integer T denoting number of test cases. First and the only line of each test case contains two space separated integers N and M denoting the number of rows and columns respectively.
For each test case, print a single integer corresponding to the answer.
- 1 ≤ T ≤ 10
- 1 ≤ N, M ≤ 2000
- Subtask 1 : 1 ≤ T ≤ 10 , 1 ≤ N,M ≤ 50 : ( 23 pts )
- Subtask 2 : 1 ≤ T ≤ 10 , 1 ≤ N,M ≤ 500 : ( 29 pts )
- Subtask 3 : 1 ≤ T ≤ 10 , 1 ≤ N,M ≤ 2000 : ( 48 pts )
Input: 3 1 1 2 2 2 3 Output: 2 25 273
Test case 1 : There are only 2 such grids possible 0 and 1.
|Tags||combinatorics, dynamic-programming, easy, june15, pavel1996|
|Time Limit:||2 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS|
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