Recenlty Luba got a credit card and started to use it. Let's consider n consecutive days Luba uses the card.

She starts with 0 money on her account.

In the evening of i-th day a transaction ai occurs. If ai > 0, then ai bourles are deposited to Luba's account. If ai < 0, then ai bourles are withdrawn. And if ai = 0, then the amount of money on Luba's account is checked.

In the morning of any of n days Luba can go to the bank and deposit any positive integer amount of burles to her account. But there is a limitation: the amount of money on the account can never exceed d.

It can happen that the amount of money goes greater than d by some transaction in the evening. In this case answer will be «-1».

Luba must not exceed this limit, and also she wants that every day her account is checked (the days when ai = 0) the amount of money on her account is non-negative. It takes a lot of time to go to the bank, so Luba wants to know the minimum number of days she needs to deposit some money to her account (if it is possible to meet all the requirements). Help her!

Input

The first line contains two integers n, d (1 ≤ n ≤ 105, 1 ≤ d ≤ 109) —the number of days and the money limitation.

The second line contains n integer numbers a1, a2, ... an ( - 104 ≤ ai ≤ 104), where ai represents the transaction in i-th day.

Output

Print -1 if Luba cannot deposit the money to her account in such a way that the requirements are met. Otherwise print the minimum number of days Luba has to deposit money.

Examples

Input

5 10
-1 5 0 -5 3


Output

0


Input

3 4
-10 0 20


Output

-1


Input

5 10
-5 0 10 -11 0


Output

2
/**
 * Created by Chirag on 17-12-2017.
 * DA-IICT (B.tech 3rd year)
 */

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


public class CreditCard {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
      
      
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */
        //The Code Starts here
        int n,Max=0,Min = 0,x,sol=0,d;
        n=sc.nextInt();
        d=sc.nextInt();
        while (n-->0)
        {
             x=sc.nextInt();
//            debug(Max,Min,x,sol);
            if(x!=0)
            {
                Max+=x;
                Min+=x;
                if(Min>d)
                {
                    System.out.println("-1");
                    return;
                }
                Max=Math.min(Max,d);

            }
            else
            {
                Min=Math.max(Min,0);
                if(Max<0)
                {
                    Max=d;
                    Min=0;
                    sol++;
                }
            }
//            debug(Max,Min,x,sol);
//            System.out.println();
        }
        System.out.println(sol);



        //The Code ends here
        out.close();
    }


/*
    int main(){
        scanf("%i%i",&n,&d);
        while(n--){
            scanf("%i",&x);
            if(x){
                Max+=x;Min+=x;
                if(Min>d) return printf("-1"),0;
                Max=min(Max,d);
            }
            else{
                Min=max(Min,0);
                if(Max<0) Max=d,Min=0,sol++;
            }
        }
        printf("%i",sol);
        return 0;
    }
*/


    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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());
        }

        char nextCharacter() {
            return next().charAt(0);
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public int[][] nextInt2DArray(int m, int n) {
            int[][] arr = new int[m][n];
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++)
                    arr[i][j] = nextInt();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }

    public static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    public static class Pair implements Comparable<Pair> {
        long u;
        long v;

        public Pair(long u, long v) {
            this.u = u;
            this.v = v;
        }


        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }

        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }

        public int compareTo(Pair other) {
            return Long.compare(u, other.u) != 0 ? Long.compare(u, other.u) : Long.compare(v, other.v);
        }

        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
    //--------------------------------------------------------


    // Different other methods

    public static long pow(long n, long p, long mod) {
        if (p == 0)
            return 1;
        if (p == 1)
            return n % mod;
        if (p % 2 == 0) {
            long temp = pow(n, p / 2, mod);
            return (temp * temp) % mod;
        } else {
            long temp = pow(n, p / 2, mod);
            temp = (temp * temp) % mod;
            return (temp * n) % mod;

        }
    }

    public static long pow(long n, long p) {
        if (p == 0)
            return 1;
        if (p == 1)
            return n;
        if (p % 2 == 0) {
            long temp = pow(n, p / 2);
            return (temp * temp);
        } else {
            long temp = pow(n, p / 2);
            temp = (temp * temp);
            return (temp * n);

        }
    }

    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }

    static long modInverse(long a, long m) {
        long m0 = m, t, q;
        long x0 = 0, x1 = 1;

        if (m == 1)
            return 0;

        while (a > 1) {
            // q is quotient
            q = a / m;

            t = m;

            // m is remainder now, process
            // same as Euclid's algo
            m = a % m;
            a = t;

            t = x0;

            x0 = x1 - q * x0;

            x1 = t;
        }

        // Make x1 positive
        if (x1 < 0)
            x1 += m0;

        return x1;
    }

    public static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    public static class DisjointSet {
        HashMap<Integer, Node> map = new HashMap<Integer, Node>();

        class Node {
            int data;
            int rank;
            Node parent;

            Node(int data) {
                this.data = data;
                this.rank = 0;
                this.parent = this;
            }
        }

        void makeSet(int data) {
            map.put(data, new Node(data));
        }

        Node findSet(int data) {
            return findSet(map.get(data));
        }

        boolean isConnected(int d1, int d2) {
            return findSet(d1) == findSet(d2);
        }

        Node findSet(Node node) {
            Node parent = node.parent;
            if (parent == node)
                return parent;
            node.parent = findSet(node.parent);
            return node.parent;
        }

        void union(int data1, int data2) {
            Node d1 = map.get(data1);
            Node d2 = map.get(data2);

            Node p1 = findSet(d1);
            Node p2 = findSet(d2);

            if (p1.data == p2.data)
                return;

            if (p1.rank >= p2.rank) {
                p1.rank = (p1.rank == p2.rank) ? p1.rank + 1 : p1.rank;
                p2.parent = p1;
            } else {
                p1.parent = p2;
            }
        }

    }


}

