Consider a permutation(^{\text{∗}}) (p_1, p_2, \ldots, p_n) of integers from (1) to (n). We can introduce the following sum for it(^{\text{†}}): ()S(p) = \sum_{1 \le l \le r \le n} \min(p_l, p_{l + 1}, \ldots, p_r)() Let us consider all permutations of length (n) with the maximum possible value of (S(p)). Output the (k)-th of them in lexicographical(^{\text{‡}})order, or report that there are less than (k) of them. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). (^{\text{†}})For example: For the permutation (1, 2, 3) the value of (S(p)) is equal to (\min(1) + \min(1, 2) + \min(1, 2, 3) + \min(2) + \min(2, 3) + \min(3) =) (1 + 1 + 1 + 2 + 2 + 3 = 10) For the permutation (2, 4, 1, 3) the value of (S(p)) is equal to (\min(2) + \min(2, 4) + \min(2, 4, 1) + \min(2, 4, 1, 3) \ +) (\min(4) + \min(4, 1) + \min(4, 1, 3) \ +) (\min(1) + \min(1, 3) \ +) (\min(3) =) (2 + 2 + 1 + 1 + 4 + 1 + 1 + 1 + 1 + 3 = 17). (^{\text{‡}})An array (a) is lexicographically smaller than an array (b) if and only if one of the following holds: (a) is a prefix of (b), but (a \ne b); or in the first position where (a) and (b) differ, the array (a) has a smaller element than the corresponding element in (b). 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 only line of each test case contains two integers (n) and (k) ((1 \le n \le 2 \cdot 10^5); (1 \le k \le 10^{12})) — the length of the permutation and the i