Chef’s girlfriend is angry with him because he forgot her birthday. Chef decided to please her by gifting her a Love Graph. 
Chef has $N$ vertices: $V_1, V_2, \dots, V_N$. Love Graph is an undirected multigraph with no self-loops and can be constructed by performing the following operations:-
- Choose an integer $i$ ($1 \leq i \leq N$)
- Choose another integer $j \space \space \{ (i \neq j) \text{ and } (1 \leq j \leq N) \}$
- Make an edge between $V_i$ and $V_j$
- Set $i = j$
- Repeat steps $2, 3$ and $4$ in order $M-1$ more times.
Find the number of ways in which Chef can construct a Love Graph. Since the answer can 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 line of each test case contains two space-separated integers $N$ and $M$.

-----Output-----
For each test case, print a single line containing one integer — the number of ways in which Chef can construct a Love Graph modulo $10^9+7$.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $2 \leq N \leq 10^9$
- $1 \leq M \leq 10^{18}$

-----Subtasks-----
- 30 points:
- $1 \leq T \leq 100$
- $2 \leq N \leq 10$
- $1 \leq M \leq 10$ 
- 70 points: original constraints

-----Sample Input-----
1

2 1   

-----Sample Output-----
2   

-----Explanation-----
There are two ways of constructing Love Graph.

In first way, we pick Vertex 1 and then join with Vertex 2.

In second way, we pick Vertex 2 and then join with Vertex 1.

Source: codechef | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
def fastpow(base, power):
	result = 1
	while power > 0:
		if power % 2 == 0:
			power = power // 2
			base = base * base
		else:
			power = power - 1
			result = result * base
			power = power // 2
			base = base * base
	return result
t = int(input())
for i in range(t):
	a = list(map(int, input().split()))
	(n, r) = (a[0], a[1])
	w = n * fastpow(n - 1, r) % (10 ** 9 + 7)
	print(w)


t = int(input())
for i in range(t):
	a = list(map(int, input().split()))
	(n, r) = (a[0], a[1])
	w = n * (n - 1) ** r % (10 ** 9 + 7)
	print(w)


from math import factorial

def p(n, r):
	return factorial(n) // factorial(n - r)
t = int(input())
for i in range(t):
	a = list(map(int, input().split()))
	(n, r) = (a[0], a[1])
	w = n * (n - 1) ** r
	print(w % (10 ** 9 + 7))


mod = 10 ** 9 + 7

def solve(n, m):
	ans = n * (n - 1) % mod
	if m == 1:
		print(ans)
		return
	else:
		ans = ans * pow(n - 1, m - 1, mod) % mod
	print(ans)
for case in range(int(input())):
	(n, m) = list(map(int, input().split()))
	solve(n, m)


mod = 1000000007

def power(n, m):
	if m == 0:
		return 1
	if m % 2 == 0:
		temp = power(n, m // 2)
		return temp * temp % mod
	else:
		temp = power(n, m // 2)
		return temp * n * temp % mod
for _ in range(int(input())):
	(n, m) = list(map(int, input().split()))
	print(n * (n - 1) * power(n - 1, m - 1) % mod)


t = int(input())
for i in range(t):
	(n, m) = list(map(int, input().split()))
	ans = n * pow(n - 1, m, 10 ** 9 + 7) % (10 ** 9 + 7)
	print(ans)