Let's call an integer array a_1, a_2, ..., a_n good if a_i ≠ i for each i.

Let F(a) be the number of pairs (i, j) (1 ≤ i < j ≤ n) such that a_i + a_j = i + j.

Let's say that an array a_1, a_2, ..., a_n is excellent if: 

  * a is good; 
  * l ≤ a_i ≤ r for each i; 
  * F(a) is the maximum possible among all good arrays of size n. 



Given n, l and r, calculate the number of excellent arrays modulo 10^9 + 7.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. 

The first and only line of each test case contains three integers n, l, and r (2 ≤ n ≤ 2 ⋅ 10^5; -10^9 ≤ l ≤ 1; n ≤ r ≤ 10^9).

It's guaranteed that the sum of n doesn't exceed 2 ⋅ 10^5.

Output

For each test case, print the number of excellent arrays modulo 10^9 + 7.

Example

Input


4
3 0 3
4 -3 5
42 -33 55
69 -42 146


Output


4
10
143922563
698570404

Note

In the first test case, it can be proven that the maximum F(a) among all good arrays a is equal to 2. The excellent arrays are: 

  1. [2, 1, 2]; 
  2. [0, 3, 2]; 
  3. [2, 3, 2]; 
  4. [3, 0, 1]. 
import sys
from sys import stdin

def modfac(n, MOD):
 
    f = 1
    factorials = [1]
    for m in range(1, n + 1):
        f *= m
        f %= MOD
        factorials.append(f)
    inv = pow(f, MOD - 2, MOD)
    invs = [1] * (n + 1)
    invs[n] = inv
    for m in range(n, 1, -1):
        inv *= m
        inv %= MOD
        invs[m - 1] = inv
    return factorials, invs

def modnCr(n,r):
    return fac[n] * inv[n-r] * inv[r] % mod

mod = 10**9+7
fac,inv = modfac(300000,mod)


tt = int(stdin.readline())
ANS = []

for loop in range(tt):

    n,l,r = map(int,stdin.readline().split())
    ans = 0

    #dont
    dmax = min(1-l,r-n)

    if dmax >= 0:
        if n % 2 == 0:
            ans += dmax * modnCr(n,n//2) % mod
        else:
            ans += 2 * dmax * modnCr(n,n//2) % mod

    #print (ans % mod,file=sys.stderr)
    #rest

    nd = dmax + 1
    while True:
        lrist = max(0,l+nd-1)
        rrist = max(0,n-(r-nd))

        #print (nd,lrist,rrist)

        if lrist + rrist > n or min(lrist,rrist) > (n+1)//2:
            break

        if n%2 == 1:
            #l is min
            uprem   = n//2 - lrist
            downrem = (n+1)//2 - rrist

            if min(uprem,downrem) >= 0:
                ans += modnCr(uprem+downrem,uprem)

            #other
            uprem   = (n+1)//2 - lrist
            downrem = n//2 - rrist

            if min(uprem,downrem) >= 0:
                ans += modnCr(uprem+downrem,uprem)

        else:
            uprem   = n//2 - lrist
            downrem = n//2 - rrist

            if min(uprem,downrem) >= 0:
                ans += modnCr(uprem+downrem,uprem)


        nd += 1

    ANS.append(str(ans % mod))

print ("\n".join(ANS))
    
