You are given a square matrix $M$ with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). Initially, all the elements of this matrix are equal to $A$. The matrix is broken down in $N$ steps (numbered $1$ through $N$); note that during this process, some elements of the matrix are simply marked as removed, but all elements are still indexed in the same way as in the original matrix. For each valid $i$, the $i$-th step consists of the following:
- Elements $M_{1, N-i+1}, M_{2, N-i+1}, \ldots, M_{i-1, N-i+1}$ are removed.
- Elements $M_{i, N-i+1}, M_{i, N-i+2}, \ldots, M_{i, N}$ are removed.
- Let's denote the product of all $2i-1$ elements removed in this step by $p_i$. Each of the remaining elements of the matrix (those which have not been removed yet) is multiplied by $p_i$.
Find the sum $p_1 + p_2 + p_3 + \ldots + p_N$. Since this number could be very large, compute it modulo $10^9+7$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $N$ and $A$.

-----Output-----
For each test case, print a single line containing one integer ― the sum of products at each step modulo $10^9+7$.

-----Constraints-----
- $1 \le T \le 250$
- $1 \le N \le 10^5$
- $0 \le A \le 10^9$
- the sum of $N$ over all test cases does not exceed $10^5$

-----Example Input-----
1
3 2

-----Example Output-----
511620149

-----Explanation-----
Example case 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 = '# cook your dish here\ntest=int(input())\nm=pow(10,9)+7\nfor _ in range(test):\n n,a=map(int,input().split())\n p=1\n f=0\n l=a\n prev=1\n for i in range(1,n+1):\n  a=l*prev\n  p=pow(a,2*i-1,m)\n  prev=(prev*p)%m\n  f=(f+p)%m\n print(f%m)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13069