github.com/captn3m0/codechef.git

---
category_name: easy
problem_code: STDYTAB
problem_name: 'Steady tables'
languages_supported:
    - ADA
    - ASM
    - BASH
    - BF
    - C
    - 'C99 strict'
    - CAML
    - CLOJ
    - CLPS
    - 'CPP 4.3.2'
    - 'CPP 4.9.2'
    - CPP14
    - CS2
    - D
    - ERL
    - FORT
    - FS
    - GO
    - HASK
    - ICK
    - ICON
    - JAVA
    - JS
    - 'LISP clisp'
    - 'LISP sbcl'
    - LUA
    - NEM
    - NICE
    - NODEJS
    - 'PAS fpc'
    - 'PAS gpc'
    - PERL
    - PERL6
    - PHP
    - PIKE
    - PRLG
    - PYTH
    - 'PYTH 3.4'
    - RUBY
    - SCALA
    - 'SCM guile'
    - 'SCM qobi'
    - ST
    - TCL
    - TEXT
    - WSPC
max_timelimit: '2'
source_sizelimit: '50000'
problem_author: pavel1996
problem_tester: null
date_added: 21-09-2014
tags:
    - combinatorics
    - dynamic
    - easy
    - june15
    - pavel1996
editorial_url: 'http://discuss.codechef.com/problems/STDYTAB'
time:
    view_start_date: 1434360600
    submit_start_date: 1434360600
    visible_start_date: 1434360600
    end_date: 1735669800
    current: 1493558190
layout: problem
---
All submissions for this problem are available.###  Read problems statements in [Mandarin Chinese](http://www.codechef.com/download/translated/JUNE15/mandarin/STDYTAB.pdf) and [Russian](http://www.codechef.com/download/translated/JUNE15/russian/STDYTAB.pdf).

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**.

### Input

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.

### Output

For each test case, print a single integer corresponding to the answer.

### Constraints

- **1** ≤ **T** ≤ **10**
- **1** ≤ **N, M** ≤ **2000**

### Subtasks

- **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 )**

### Example

<pre>
<b>Input:</b>
3
1 1
2 2
2 3
<b>Output:</b>
2
25
273
</pre>### Explanation

Test case 1 : There are only 2 such grids possible 0 and 1.