Bus Video System

The busses in Berland are equipped with a video surveillance system. The system records information about changes in the number of passengers in a bus after stops.

If x is the number of passengers in a bus just before the current bus stop and y is the number of passengers in the bus just after current bus stop, the system records the number y-x. So the system records show how number of passengers changed.

The test run was made for single bus and n bus stops. Thus, the system recorded the sequence of integers a₁, a₂, ..., a_n (exactly one number for each bus stop), where a_i is the record for the bus stop i. The bus stops are numbered from 1 to n in chronological order.

Determine the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to w (that is, at any time in the bus there should be from 0 to w passengers inclusive). 

The first line contains two integers n and w (1 <= n <= 1000, 1 <= w <= 10⁹) — the number of bus stops and the capacity of the bus.

The second line contains a sequence a₁, a₂, ..., a_n (-10⁶<= a_i <= 10⁶), where a_i equals to the number, which has been recorded by the video system after the i-th bus stop.

Print the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to w. If the situation is contradictory (i.e. for any initial number of passengers there will be a contradiction), print 0.

3 5
2 1 -3

3

2 4
-1 1

4

4 10
2 4 1 2

2

 Note

In the first example initially in the bus could be 0, 1 or 2 passengers.
In the second example initially in the bus could be 1, 2, 3 or 4 passengers.
In the third example initially in the bus could be 0 or 1 passenger.