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-----
Input:
3
1 1
2 2
2 3
Output:
2
25
273

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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\n \nMOD = 1000000000\n \nT = int(sys.stdin.readline())\n \n \ndef gcd(a, b):\n return a if b == 0 else gcd(b, a % b)\n \n \ndef solve(n, r):\n if r > n - r:\n  r = n - r\n \n num = 1\n den = 1\n j = 1\n for i in range(n - r + 1, n + 1):\n  num *= i\n  den *= j\n  j += 1\n \n return (num / den) % MOD\n \nfor t in range(T):\n n, r = list(map(int, sys.stdin.readline().split()))\n t=r-1\n q=0\n li=[]\n for i in range(r+1):\n  li.append(solve(t,q))\n  t+=1\n  q+=1\n arr=li[:]\n temp=0\n for i in range(1,n):\n  summ=sum(arr)\n  for j in range(r+1):\n   if(j==0):\n    summ+=0\n   else:\n    summ-=temp\n   temp=arr[j]\n   arr[j]=(li[j]*(summ%MOD))%MOD\n print(sum(arr)%MOD) '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13445