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 Solution {
	public final static int MOD = 1000000007;
	public static int count = 0;
	public static int dx[] = {0,1,-1};
	public static int dy[] = {0,1,-1};
	public static int max = 0;
	public static boolean flag;
	public static LinkedList<Integer> adj[];
	@SuppressWarnings("unchecked")
	public static void main(String[] args) throws IOException {
		InputReader scan = new InputReader(System.in);
	   	OutputStream outputStream = System.out;
	   	PrintWriter pw = new PrintWriter(outputStream);
	   	StringBuilder sb = new StringBuilder();
	   	int n = scan.nextInt();
	   	int w = scan.nextInt();
	   	int min = Integer.MAX_VALUE;
	   	int max = Integer.MIN_VALUE;
	   	int sum = 0;
	   	while(n-->0)
	   	{
	   		sum+=scan.nextInt();
	   		min = Math.min(min, sum);
	   		max = Math.max(max, sum);
	   	}
	   	//System.out.println(max+" "+min);
	   	int count = w+1;
	   	if(max>0)
	   		count-=Math.min(max, count);
	   	if(min<0)
	   		count+=Math.max(-count, min);
	   	pw.println(count);
	   	pw.close();
	}
	public static int[][] graph(int from[],int to[],int m,int n)
	{
		int[][] g = new int[n+1][];
		int count[] = new int[n+1];
		Arrays.fill(count, 0);
		for(int i=0;i<m;i++)
		{
			count[from[i]]++;
			count[to[i]]++;
		}
		for(int i=0;i<n+1;i++)
			g[i] = new int[count[i]];
		Arrays.fill(count, 0);
		for(int i=0;i<m;i++)
		{
			g[from[i]][count[from[i]]++] = to[i];
			g[to[i]][count[to[i]]++] = from[i];
		}
		return g;
	}
	public static int binarySearch(long arr[],long key,long pre)
	{
		int l = 1, r = arr.length-1;
		while(l<=r)
		{
			int mid = (l+r)/2;
			if(arr[mid]-pre==key)
			{
				r = mid;
				break;
			}
			if(arr[mid]-pre>key)
				r = mid-1; 
			else
				l = mid+1;
		}
		return r;
	}
	public static void inOrder(int i,int arr[],int n,ArrayList<Integer> ans)
	{
		if(i<n)
		{
			inOrder(2*i+1,arr,n,ans);
			ans.add(arr[i]);
			inOrder(2*i+2,arr,n,ans);
		}
	}
	public static int find(int x,int parent[])
	{
		if(parent[x]!=x)
			parent[x] = find(parent[x],parent);
		return parent[x];
	}
	public static void union(int parent[],int x,int y)
	{
		int xParent = find(x,parent);
		int yParent = find(y,parent);
		parent[xParent] = yParent;
	}
	public static void dfs(int x,boolean visited[],int[][] g)
	{
		visited[x] = true;
		if(g[x].length!=2)
			flag = false;
		for(int i=0;i<g[x].length;i++)
		{
			int temp = g[x][i];
			if(!visited[temp])
				dfs(temp,visited,g);
		}
	}
	public static void buildTree(int arr[],int tree[],int node,int start,int end)
	{
		if(start==end)
		{
			tree[node] = arr[start];
			return;
		}
		int mid = (start+end)/2;
		buildTree(arr,tree,2*node,start,mid);
		buildTree(arr,tree,2*node+1,mid+1,end);
		tree[node] = tree[2*node]+tree[2*node+1];
	}
	public static void update(int arr[],int tree[],int node,int inx,int val,int start,int end)
	{ 
		if(start==end)
		{
			tree[node] = val;
			arr[inx] = val;
			return;
		}
		int mid = (start+end)/2;
		if(inx<=mid)
			update(arr,tree,2*node,inx,val,start,mid);
		else
			update(arr,tree,2*node+1,inx,val,mid+1,end);
		tree[node] = tree[2*node]+tree[2*node+1];
	}
	public static int query(int tree[],int node,int l,int r,int start,int end)
	{
		if(r<start || l>end)
			return 0;
		if(l<=start && end<=r)
			return tree[node];
		int mid = (start+end)/2;
		int ans1 = query(tree,2*node,l,r,start,mid);
		int ans2 = query(tree,2*node+1,l,r,mid+1,end);
		return ans1+ans2;
	}
	public static void merge(int arr[],int start,int mid,int end)
	{
		int l = start, r = mid+1;
		int temp[] = new int[end-start+1];
		int k = 0;
		for(int i=start;i<=end;i++)
		{
			if(l>mid)
				temp[k++] = arr[r++];
			else if(r>end)
				temp[k++] = arr[l++];
			else if(arr[l]<=arr[r])
				temp[k++] = arr[l++];
			else{
				temp[k++] = arr[r++];
				count+=(mid-l+1);
			}
		}
		for(int i=0;i<k;i++)
			arr[start++] = temp[i];
	}
	public static void mergeSort(int arr[],int l,int r)
	{
		if(l<r){
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,mid,r);
		}
	}
	public static void sieve(int spf[],int n)
	{
		for(int i=1;i<=n;i++)
			spf[i] = i;
		for(int i=2;i*i<=n;i++)
		{
			if(spf[i]==i)
			{
				for(int j=i;j<=n;j+=i)
					if(spf[j]==j)
						spf[j] = i;
			}
		}
	}
	public static void factors(int n,int spf[],ArrayList<Integer> factors)
	{
		int pre = 0;
		while(n!=1)
		{
			int temp = spf[n];
			if(temp!=pre)
			{
				factors.add(temp);
				pre = temp;
			}
			n/=temp;
		}
	}
	public static boolean isPrime(int n)
	{
		if(n==0 || n==1)
			return false;
		int limit = (int)Math.sqrt(n);
		for(int i=2;i<=limit;i++)
		{
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static long pow(long a,long b,int m)
	{
		long result = 1;
		while(b>0)
		{
			if(b%2==1)
				result = ((result%m)*(a%m))%m;
			a = ((a%m)*(a%m))%m;
			b/=2;
		}
		return result;
	}
	public static long mulinv(long a,long m)
	{
		long arr[] = new long[2];
		long gcd = gcdExtended(a,m,arr);
		if(gcd==1)
			return (arr[0]%m+m)%m;
		else
			return Integer.MAX_VALUE;
	}
	public static long gcdExtended(long a,long b,long arr[])
	{
		if (a == 0)
	    {
	        arr[0] = 0;
	        arr[1] = 1;
	        return b;
	    }
	    long gcd = gcdExtended(b%a, a, arr);
	    long temp = arr[0];
	    arr[0] = arr[1] - (b/a) * arr[0];
	    arr[1] = temp;
	    return gcd;
	}
	public static long kadane(int items[])
	{
		int n = items.length;
		long max = (long)items[0];
		long curr_max = (long)items[0];
		for(int i=1;i<n;i++)
		{
			curr_max = Math.max((long)curr_max+items[i], items[i]);
			max = Math.max(max, curr_max);
		}
		return max;
	}
	public static int gcd(int a,int b)
	{
		if(b==0)
			return a;
		return gcd(b,a%b);
	}
	public static int LCS(String s1,String s2) //Longest common subsequence
	{
		int n = s1.length();
		int m = s2.length();
		int lcs[][] = new int[n+1][m+1];
		for(int i=0;i<=n;i++)
		{
			for(int j=0;j<=m;j++)
			{
				if(i==0 || j==0)
					lcs[i][j] = 0;
				else if(s1.charAt(i-1)==s2.charAt(j-1))
					lcs[i][j] = lcs[i-1][j-1] + 1;
				else
					lcs[i][j] = Math.max(lcs[i][j-1], lcs[i-1][j]);
			}
		}
		return lcs[n][m];
	}
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}
class InputReader {
    public BufferedReader reader;
	public StringTokenizer tokenizer;
    public InputReader(InputStream inputstream) {
        reader = new BufferedReader(new InputStreamReader(inputstream));
		tokenizer = null;
	}
    public String nextLine(){
        String fullLine=null;
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
		    try {
		        fullLine=reader.readLine();
		    } catch (IOException e) {
    			throw new RuntimeException(e);
    			}
        		return fullLine;
        }
		return fullLine;
	}
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
    			tokenizer = new StringTokenizer(reader.readLine());
    		} catch (IOException e) {
        		throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
    public long nextLong() {
        return Long.parseLong(next());
	}
	public int nextInt() {
		return Integer.parseInt(next());
	}
}

class Pair{
	int val, ind;
	Pair(int x,int y)
	{
		val = x;
		ind = y;
	}
}