On a mysterious island, Captain Flint left a treasure map, which contains clues in the form of a sequence of numbers — an array a. The pirates have a starting value x that they need to transform by following all the steps on the map to reach the treasure.

For each value of x that they choose, the pirates go through the array a from start to finish and perform the following actions for each element of the array:

Thus, at the end of the route, the value of x becomes a new number indicating the location of the treasure.

Unfortunately, the pirates turned out to be very weak in mathematics (although they can count bottles of rum perfectly), so they asked you for help in finding the treasure. They have q numbers, possible starting values of x. You need to output for each of these numbers the result obtained after performing the actions described above.

The first line contains 2 integers n, q — the number of elements in the array a and the number of possible starting values (1 ≤ n, q ≤ 10⁶).

The second line contains n integers separated by spaces, defining the array a. (|a_i| ≤ 10⁶).

In the following q lines, each contains one integer x_i — the possible starting values. (|x_i| ≤ 10⁶).

Output q lines. In the i-th line, output a single number — the number obtained after performing all actions on the number x_i.