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 a_1, a_2, ..., 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).

Input

The first line contains two integers n and w (1 ≤ n ≤ 1 000, 1 ≤ w ≤ 10^{9}) — the number of bus stops and the capacity of the bus.

The second line contains a sequence a_1, a_2, ..., a_n (-10^{6} ≤ a_i ≤ 10^{6}), where a_i equals to the number, which has been recorded by the video system after the i-th bus stop.

Output

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.

Examples

Input

3 5
2 1 -3


Output

3


Input

2 4
-1 1


Output

4


Input

4 10
2 4 1 2


Output

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.
import java.io.*;
import java.util.*;

public class mymy
{	

	public static void main(String[] Rohan)throws IOException
	{
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] s=br.readLine().split(" ");
		int n=Integer.parseInt(s[0]);long w=Long.parseLong(s[1]);
		long[] a=new long[n];
		s=br.readLine().split(" ");
		for(int i=0;i<n;i++)
		{
			a[i]=Long.parseLong(s[i]);
		}

		long low=0,high=w,mid=0,ansh=(int)Double.NEGATIVE_INFINITY;
		while(low<=high)
		{
			mid=(low+high)/2;

			boolean check=true;
			long sum=mid;
			for(int i=0;i<n;i++)
			{
				sum+=a[i];
				if(sum>w)
				{
					check=false;break;
				}
			}
			if(check)
			{
				low=mid+1;ansh=mid;
			}
			else
			{
				high=mid-1;
			}
			//System.out.println(ansh+" "+low+" "+high);
		}
		low=0;high=10000000000L;mid=0;long anst=(int)Double.POSITIVE_INFINITY;
		//System.out.println("--");

		while(low<=high)
		{
			mid=(low+high)/2;

			boolean check=true;
			long sum=mid;
			for(int i=0;i<n;i++)
			{
				sum+=a[i];
				if(sum<0)
				{
					check=false;break;
				}
			}
			if(check)
			{
				anst=mid;high=mid-1;
			}
			else
			{
				low=mid+1;
			}
			//System.out.println(anst+" "+low+" "+high);
		}
		long aa=ansh-anst+1;
		if(aa<0)
			System.out.println(0);
		else
			System.out.println(aa);
			
		
	}
}	

