Problem: Polycarp is an experienced participant in Codehorses programming contests. Now he wants to become a problemsetter.

He sent to the coordinator a set of n problems. Each problem has it's quality, the quality of the i-th problem is ai (ai can be positive, negative or equal to zero). The problems are ordered by expected difficulty, but the difficulty is not related to the quality in any way. The easiest problem has index 1, the hardest problem has index n.

The coordinator's mood is equal to q now. After reading a problem, the mood changes by it's quality. It means that after the coordinator reads a problem with quality b, the value b is added to his mood. The coordinator always reads problems one by one from the easiest to the hardest, it's impossible to change the order of the problems.

If after reading some problem the coordinator's mood becomes negative, he immediately stops reading and rejects the problemset.

Polycarp wants to remove the minimum number of problems from his problemset to make the coordinator's mood non-negative at any moment of time. Polycarp is not sure about the current coordinator's mood, but he has m guesses "the current coordinator's mood q = bi".

For each of m guesses, find the minimum number of problems Polycarp needs to remove so that the coordinator's mood will always be greater or equal to 0 while he reads problems from the easiest of the remaining problems to the hardest.

Input

The first line of input contains two integers n and m (1 ≤ n ≤ 750, 1 ≤ m ≤ 200 000) — the number of problems in the problemset and the number of guesses about the current coordinator's mood.

The second line of input contains n integers a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — the qualities of the problems in order of increasing difficulty.

The third line of input contains m integers b1, b2, ..., bm (0 ≤ bi ≤ 1015) — the guesses of the current coordinator's mood q.

Output

Print m lines, in i-th line print single integer — the answer to the problem with q = bi.

Example

Input

6 3
8 -5 -4 1 -7 4
0 7 3


Output

2
0
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;


public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Parser in = new Parser(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        public static PriorityQueue queue;

        public static int solutionBinarySearch(long[] values, long n) {
            int start = 0;
            int end = values.length - 1;

            while (start <= end) {
                int mid = (start + end) / 2;

                if (values[mid] >= n) {
                    end = mid - 1;
                } else if (values[mid] < n) {
                    start = mid + 1;
                }
            }

            return start;
        }

        public static long binarySearch(long[] values, int removed) {
            long low = -1000000000000L;
            long high = 1000000000000L;

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

                if (!verify(values, removed, mid)) {
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }

            return high;
        }

        public static boolean verify(long[] values, int removed, long target) {
            //If we can remove "removed" number of values from array values, can the minimum prefix sum be greater than or equal to target?'

            queue.clear();

            int count = 0;
            long sum = 0;
            for (int i = 0; i < values.length; i++) {
                sum += values[i];
                queue.add(values[i]);
                while (sum < target) {
                    if (!queue.isEmpty()) {
                        sum -= queue.remove();
                        count++;
                    } else return false;
                }
            }

            return count <= removed;
        }

        public void solve(int testNumber, Parser in, OutputWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();

            long[] values = new long[n];
            queue = new PriorityQueue(n);

            for (int i = 0; i < n; i++) {
                values[i] = in.nextInt();
            }

            long[] dp = new long[n + 1]; //dp[i] represents the maximum minimum prefix sum you can obtain with i removed objects

            for (int i = 0; i < n + 1; i++) {
                dp[i] = binarySearch(values, i);
            }
            dp[n] = 0;

            for (int i = 0; i < m; i++) {
                long q = in.nextLong();
                out.println(solutionBinarySearch(dp, -q));

			/*
            int index = Arrays.binarySearch(dp, -q);

			if (index >= 0) {
				w.println(index);
			} else {
				w.println(-index - 1);
			}*/
            }
        }

        public class PriorityQueue {
            private int size = 0;
            private long[] elements;

            public PriorityQueue(int capacity) {
                elements = new long[capacity];
            }

            public boolean isEmpty() {
                return size == 0;
            }

            public void add(long element) {
                elements[size] = element;
                shiftUp(size++);
            }

            public void shiftUp(int index) {
                long value = elements[index];
                while (index != 0) {
                    int parent = (index - 1) >>> 1;
                    long parentValue = elements[parent];
                    if (parentValue <= value) {
                        elements[index] = value;
                        return;
                    }
                    elements[index] = parentValue;
                    index = parent;
                }
                elements[0] = value;
            }

            public void shiftDown(int index) {
                if (index < 0 || index >= size) {
                    throw new IllegalArgumentException();
                }
                while (true) {
                    int child = (index << 1) + 1;
                    if (child >= size) {
                        return;
                    }
                    if (child + 1 < size && elements[child] > elements[child + 1]) {
                        child++;
                    }
                    if (elements[index] <= elements[child]) {
                        return;
                    }
                    swap(index, child);
                    index = child;
                }
            }

            private void swap(int first, int second) {
                long temp = elements[first];
                elements[first] = elements[second];
                elements[second] = temp;
            }

            public long remove() {
                if (isEmpty()) {
                    throw new IndexOutOfBoundsException();
                }
                long result = elements[0];
                if (size == 1) {
                    size = 0;
                    return result;
                }
                elements[0] = elements[--size];
                shiftDown(0);
                return result;
            }

            public void clear() {
                size = 0;
            }

        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(Writer out) {
            super(out);
        }

        public OutputWriter(OutputStream out) {
            super(out);
        }

    }

    static class Parser {
        private BufferedReader din;
        private StringTokenizer tokenizer;

        public Parser(InputStream in) {
            din = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(din.readLine());
                } catch (Exception e) {
                    throw new UnknownError();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}