There are N boxes arranged in a row. Initially, the i-th box from the left contains ai candies.
Snuke can perform the following operation any number of times:
Choose a box containing at least one candy, and eat one of the candies in the chosen box.
His objective is as follows:
Any two neighboring boxes contain at most x candies in total.
Find the minimum number of operations required to achieve the objective.
Constraints
2≤N≤105
0≤ai≤109
0≤x≤109
Input
The input is given from Standard Input in the following format:
N X
a1 a2 ..... aN
Output
Print the minimum number of operations required to achieve the objective.
Eat one candy in the second box. Then, the number of candies in each box becomes (2,1,2)