A non-decreasing sequence is a called a Fox sequence, iff the most frequent element in the sequence is unique. 

e.g. The sequence 1, 1, 2, 3, 4  is a Fox sequence, because it follows the above definition. The most frequent element is 1. It occurs twice in the series, and is unique.

But the sequence 1, 1, 2, 2 is not a Fox sequence, because there are two most frequent elements - 1 and 2. It violates the uniqueness property.

Note: Sequence 2, 1, 1 is not a Fox sequence, because it is not a non-decreasing sequence.

You need to find the number of all possible Fox sequences of length n with elements having value between lo and hi inclusive.  

As the number can grow very large, return the number modulo (10^{9} + 7).

Input Format 

The first line will contain T, i.e., the number of test cases. 

For each test case, there will be a single line containing three space separated integers n, lo, hi.

Output Format 

For each test case, display a single value corresponding to the number of all possible Fox sequences.

Constraints  

1  ≤ T ≤ 5 

1  ≤ lo, hi ≤ 10^{9} 

lo ≤ hi 

0  ≤ \|hi - lo\| < 10^{5} 

1  ≤ n ≤ 10^{5}  

Sample Input

5
2 1 1
2 1 3
3 1 2
4 4 5
10 2 4

Sample Output

1
3
4
4
60

Explanation 

For the first test case, 1 1 is the only possible Fox sequence. 

For the second test case, 1 1, 2 2, and 3 3 are three possible Fox sequences. 

For the third test case, 1 1 1, 2 2 2, 1 1 2, and 1 2 2 are four possible Fox 

sequences. 

Rest of the test cases are up to you to figure out.

Difficulty: MEDIUM
Tags: Combinatorics

Starter code:

Solutions:
import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


MOD = 1000000007

def inv(x):
	return pow(x, MOD - 2, MOD)
f = [1]
fi = [1]
for i in range(1, 200001):
	n = f[i - 1] * i % MOD
	f.append(n)
	fi.append(inv(n))

def C(n, k):
	if n < k:
		return 0
	return f[n] * fi[k] * fi[n - k] % MOD

def R(N, n, k):
	if n * k < N:
		result = 0
	elif N == 0:
		result = 1
	elif n < 0 or k < 0:
		result = 0
	elif n * k == N:
		result = 1
	else:
		result = 0
		s = 0
		sk = 0
		sign = 1
		while sk <= N:
			result = (result + sign * C(n, s) * C(n + N - sk - 1, N - sk)) % MOD
			s += 1
			sk += k + 1
			sign = -sign
	return result

def solve(N, n):
	result = 0
	for k in range(0, N + 1):
		result = (result + R(N - k, n - 1, k - 1)) % MOD
	return n * result % MOD
for _ in range(int(input())):
	(N, lo, hi) = list(map(int, input().split()))
	print(solve(N, hi - lo + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))


import sys
P = 10 ** 9 + 7
fact = [1]
for i in range(1, 200001):
	fact.append(fact[-1] * i % P)
inv = [0, 1]
for i in range(2, 200001):
	inv.append(P - P // i * inv[P % i] % P)
inv_fact = [1]
for i in range(1, 100001):
	inv_fact.append(inv_fact[-1] * inv[i] % P)

def ceil_div(a, b):
	return -(-a // b)

def part(n, k):
	if k == 0:
		return 1 if n == 0 else 0
	return C(n + k - 1, n)

def C(n, k):
	return fact[n] * inv_fact[k] % P * inv_fact[n - k] % P if n >= 0 and k >= 0 and (k <= n) else 0

def g(sum, n, b):
	ret = 0
	for i in range(sum // b + 1):
		sign = 1 if i & 1 == 0 else -1
		ret += sign * part(sum - i * b, n) * C(n, i) % P
		ret %= P
	return ret

def f(n, k):
	ret = 0
	for max in range(ceil_div(n + k - 1, k), n + 1):
		ret += g(n - max, k - 1, max)
		ret %= P
	return ret * k % P
t = int(input())
for _ in range(t):
	(n, low, high) = map(int, input().split())
	print(f(n, high - low + 1))