Hamid wrote (3014) lines of code for the a+b problem and gave (10) lines of it to Hamed; then the following problem came to Hamed's mind. You are given two integers (n) and (m). An array (a_1,a_2,\ldots,a_n) is called snake if and only if all of the following conditions hold: All elements in (a) are integers between (0) and (m); (a_1 + a_2 + \cdots + a_n = m); (a_n=\max\left(a_1, a_2, \ldots, a_n\right)). We define (f(a)) as in the following pseudocode: Find the sum of (f(a)) over all snake arrays (a_1,a_2,\ldots,a_n), modulo (10^9+7). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains two integers (n) and (m) ((2 \leq n \leq 2 \cdot 10^5), (0 \leq m \leq 2 \cdot 10^5)) — the length of a snake array and the sum of all elements in a snake array. It is guaranteed that the sum of (m) over all test cases does not exceed (2 \cdot 10^5). For each test case, output a single integer — the sum of (f(a)) over all snake arrays (a_1,a_2,\ldots,a_n), modulo (10^9+7). In the first test case, there are three snake arrays: (f(0, 5) = 5); (f(1, 4) = 3); (f(2, 3) = 1). Thus, the answer is (5+3+1=9). In the second test case, there are six snake arrays: (f(0, 0, 4) = 4); (f(0, 1, 3) = 3); (f(1, 0, 3) = 2); (f(1, 1, 2) = 1); (f(0, 2, 2) = 2); (f(2, 0, 2) = 2). Thus, the answer is (4+3+2+1+2+2=14). In the fifth test case, a possible snake array is: (f(3, 1, 4, 1, 5, 9) = 6).