Tit for Tat (Codeforces 1516A)
Tags: Greedy, greedy

Given an array $$$a$$$ of length $$$n$$$, you can do at most $$$k$$$ operations of the following type on it:  choose $$$2$$$ different elements in the array, add $$$1$$$ to the first, and subtract $$$1$$$ from the second. However, all the elements of $$$a$$$ have to remain non-negative after this operation. What is lexicographically the smallest array you can obtain?An array $$$x$$$ is lexicographically smaller than an array $$$y$$$ if there exists an index $$$i$$$ such that $$$x_i<y_i$$$, and $$$x_j=y_j$$$ for all $$$1 \le j < i$$$. Less formally, at the first index $$$i$$$ in which they differ, $$$x_i<y_i$$$.

Input: The first line contains an integer $$$t$$$ ($$$1 \le t \le 20$$$) – the number of test cases you need to solve.The first line of each test case contains $$$2$$$ integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 100$$$, $$$1 \le k \le 10000$$$) — the number of elements in the array and the maximum number of operations you can make.The second line contains $$$n$$$ space-separated integers $$$a_1$$$, $$$a_2$$$, $$$\ldots$$$, $$$a_{n}$$$ ($$$0 \le a_i \le 100$$$) — the elements of the array $$$a$$$.

Output: For each test case, print the lexicographically smallest array you can obtain after at most $$$k$$$ operations.

Note: In the second test case, we start by subtracting $$$1$$$ from the first element and adding $$$1$$$ to the second. Then, we can't get any lexicographically smaller arrays, because we can't make any of the elements negative.

Sample Inputs:
2
3 1
3 1 4
2 10
1 0

Sample Outputs:
2 1 5 
0 1

Solution (Python):
for _ in range(int(input())):
    (n, k) = map(int, input().split())
    l = list(map(int, input().split()))
    for i in range(n - 1):
        if l[i] <= k:
            k -= l[i]
            l[-1] += l[i]
            l[i] = 0
        else:
            l[-1] += k
            l[i] -= k
            k = 0
    print(*l)

Solution (Python):
t = int(input())
for _ in range(t):
    (n, k) = map(int, input().split())
    v = list(map(int, input().split()))
    for i in range(n - 1):
        m = min(k, v[i])
        v[i] -= m
        v[-1] += m
        k -= m
    print(*v, sep=' ')

Solution (Python):
def smallest_lexicographically_array(n, k, a):
    i = 0
    while k > 0 and i < n - 1:
        diff = min(k, a[i])
        a[i] -= diff
        a[n - 1] += diff
        k -= diff
        i += 1
    return ' '.join(map(str, a))

def main():
    t = int(input().strip())
    for _ in range(t):
        (n, k) = map(int, input().strip().split())
        a = list(map(int, input().strip().split()))
        result = smallest_lexicographically_array(n, k, a)
        print(result)
if __name__ == '__main__':
    main()