Scoreboard Digit Increment

An arena's digital scoreboard displays the home team's running point total as a row of individual digit tiles, most significant digit first, with no leading-zero tile unless the total itself is exactly zero. After a scoring play worth k points, the operator needs the new tile arrangement without ever reconstructing the whole number as a single machine integer internally tile-by-tile — the update must work directly on the digit tiles the way the physical board does, propagating any carry leftward.

Given the current digit tiles and the point increment k, compute the digit tiles of current_value + k.

Input format

Line 1: an integer n, the number of digit tiles. Line 2: n space-separated integers d_1 d_2 ... d_n (each 0 <= d_i <= 9), the current digits most significant first. d_1 is not 0 unless n == 1. Line 3: an integer k, the number of points to add.

Output format

A single line of space-separated digits, most significant first, representing current_value + k, with no leading zeros (print a single 0 if the result is exactly zero).

Constraints

1 <= n <= 10000. 0 <= k <= 10000.

3
1 2 0
34

1 5 4

1
0
0

0