Given an array (a), define (f(a)) as follows: Let (k) be an integer with (1 \leq k \leq n). Partition (a) into (k) subarrays(^{\text{∗}}) (s_1,s_2,\ldots,s_k) such that (s_1+s_2+\ldots+s_k=a). Here, (+) represents array concatenation. Let (b) be an empty array. For each (i) from (1) to (k) in order, append the minimum element of (s_i) to the end of (b). Over all possible (k) and partitions, (f(a)) is the value of (k) such that there exists a partition that produces the lexicographically largest (b)(^{\text{†}}). You are given (n) integers (x_1,x_2,\ldots,x_n). Please determine if there exists a permutation(^{\text{‡}}) (a) such that (f(a_1,a_2,\ldots,a_i)=x_i) for each (1 \leq i \leq n). If there is a permutation, print one. If there are multiple possible answers, you may output any one. (^{\text{∗}})An array (c) is a subarray of an array (d) if (c) can be obtained from (d) by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. (^{\text{†}})An array (c) is lexicographically smaller than an array (d) if and only if one of the following holds: (c) is a prefix of (d), but (c \ne d); or in the first position where (c) and (d) differ, the array (c) has a smaller element than the corresponding element in (d). (^{\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). 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 c