B'You have an array a of size n , initially filled with zeros ( a_1 = a_2 = ldots = a_n = 0 ). You also have an array of integers c of size n . Initially, you have k coins. By paying c_i coins, you can add 1 to all elements of the array a from the first to the i -th element ( a_j mathrel{+}= 1 for all 1 <= q j <= q i ). You can buy any c_i any number of times. A purchase is only possible if k geq c_i , meaning that at any moment k geq 0 must hold true. Find the lexicographically largest array a that can be obtained. An array a is lexicographically smaller than an array b of the same length if and only if in the first position where a and b differ, the element in array a is smaller than the corresponding element in b . The first line contains a single integer t ( 1 <= q t <= q 10^4 ) -- the number of test cases. This is followed by a description of the test cases. The first line of each test case contains a single integer n ( 1 <= q n <= q 2 cdot 10^5 ) -- the size of arrays a and c . The second line of each test case contains n integers c_1, c_2, ldots, c_n ( 1 <= q c_i <= q 10^9 ) -- the array c . The third line of each test case contains a single integer k ( 1 <= q k <= q 10^9 ) -- the number of coins you have. It is guaranteed that the sum of all n values across all test cases does not exceed 2 cdot 10^5 . For each test case, output n integers a_1, a_2, ldots, a_n -- the lexicographically largest array a that can be obtained. In the first test case, a_1 cannot be greater than 5 , and if we buy c_1 five times, we will run out of money, so a = [5, 0, 0] . In the second test case, a_1 cannot be greater than 2 , but we can buy c_1 and c_2 once each (buying c_2 twice is not possible), so'...