Aryan and Harshith play a game. They both start with three integers (a), (b), and (k). Aryan then gives Harshith two integers (n) and (m). Harshith then gives Aryan a matrix (X) with (n) rows and (m) columns, such that each of the elements of (X) is between (1) and (k)(inclusive). After that, Aryan wins if he can find a submatrix(^{\text{∗}}) (Y) of (X) with (a) rows and (b) columns such that all elements of (Y) are equal. For example, when (a=2, b=2, k=6, n=3) and (m=3), if Harshith gives Aryan the matrix below, it is a win for Aryan as it has a submatrix of size (2\times 2) with all elements equal to (1) as shown below. Aryan gives you the values of (a), (b), and (k). He asks you to find the lexicographically minimum tuple ((n,m)) that he should give to Harshith such that Aryan always wins. Help Aryan win the game. Assume that Harshith plays optimally. The values of (n) and (m) can be large, so output them modulo (10^9+7). A tuple ((n_1, m_1)) is said to be lexicographically smaller than ((n_2, m_2)) if either (n_1<n_2) or (n_1=n_2) and (m_1<m_2). (^{\text{∗}})A submatrix of a matrix is obtained by removing some rows and/or columns from the original matrix. 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. Each test case contains a single line with three space-separated integers (a, b) and (k) ((1\leq a,b,k\leq 10^5)). It is guaranteed that the sum of (\max(a, b, k)) over all test cases does not exceed (10^5). For each test case, output a single line containing two space-separated integers (n) and (m), denoting the answer to the problem. The values of (n) and (m) can be large, so output them modulo (10^9+7). For the first test case, every (n\times m) matrix contai