Once upon a time DravDe, an outstanding person famous for his professional achievements (as you must remember, he works in a warehouse storing Ogudar-Olok, a magical but non-alcoholic drink) came home after a hard day. That day he had to drink 9875 boxes of the drink and, having come home, he went to bed at once.

DravDe dreamt about managing a successful farm. He dreamt that every day one animal came to him and asked him to let it settle there. However, DravDe, being unimaginably kind, could send the animal away and it went, rejected. There were exactly n days in DravDe’s dream and the animal that came on the i-th day, ate exactly ci tons of food daily starting from day i. But if one day the animal could not get the food it needed, it got really sad. At the very beginning of the dream there were exactly X tons of food on the farm.

DravDe woke up terrified...

When he retold the dream to you, he couldn’t remember how many animals were on the farm by the end of the n-th day any more, but he did remember that nobody got sad (as it was a happy farm) and that there was the maximum possible amount of the animals. That’s the number he wants you to find out. 

It should be noticed that the animals arrived in the morning and DravDe only started to feed them in the afternoon, so that if an animal willing to join them is rejected, it can’t eat any farm food. But if the animal does join the farm, it eats daily from that day to the n-th.

Input

The first input line contains integers n and X (1 ≤ n ≤ 100, 1 ≤ X ≤ 104) — amount of days in DravDe’s dream and the total amount of food (in tons) that was there initially. The second line contains integers ci (1 ≤ ci ≤ 300). Numbers in the second line are divided by a space.

Output

Output the only number — the maximum possible amount of animals on the farm by the end of the n-th day given that the food was enough for everybody.

Examples

Input

3 4
1 1 1


Output

2


Input

3 6
1 1 1


Output

3

Note

Note to the first example: DravDe leaves the second and the third animal on the farm. The second animal will eat one ton of food on the second day and one ton on the third day. The third animal will eat one ton of food on the third day.
import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringTokenizer;
 
public class Main1 {
 
	static int c[], n, memo[][];
	static boolean v[][];
 
	static final int _INF = (int) -1e5;
 
	static int solve(int indx, int rem) {
		if (rem < 0)
			return _INF;
		if (indx >= n) {
			return 0;
		}
		if (v[indx][rem]) {
			return memo[indx][rem];
		}
		v[indx][rem] = true;
 
		int take = 1 + solve(indx + 1, (rem - (n - indx) * c[indx]));
		int leave = solve(indx + 1, rem);
 
		return memo[indx][rem] = Math.max(take, leave);
	}
 
	public static void main(String[] args) throws IOException {
		FastReader input = new FastReader();
		PrintWriter out = new PrintWriter(new File("output.txt"));
		n = input.nextInt();
		int x = input.nextInt();
		c = new int[n];
 
		for (int i = 0; i < n; i++) { c[i] = input.nextInt(); }
		memo = new int[n + 1][x + 1];
		v = new boolean[n + 1][x + 1];
		int ans = solve(0, x);
		out.println(ans);
		out.flush();
 
	}
 
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader() {
			try {
				br = new BufferedReader(new FileReader(new File("input.txt")));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
			// br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() throws IOException {
			while (st == null || !st.hasMoreElements()) { st = new StringTokenizer(br.readLine()); }
			return st.nextToken();
		}
 
		int nextInt() throws NumberFormatException, IOException { return Integer.parseInt(next()); }
 
		long nextLong() throws NumberFormatException, IOException { return Long.parseLong(next()); }
 
		double nextDouble() throws NumberFormatException, IOException { return Double.parseDouble(next()); }
 
		String nextLine() throws IOException {
			String str = "";
			str = br.readLine();
			return str;
		}
 
		boolean hasNext() throws IOException { return br.ready(); }
	}
 
	static class con {
		static int IINF = (int) 1e9;
		static int _IINF = (int) -1e9;
		static long LINF = (long) 1e15;
		static long _LINF = (long) -1e15;
		static double EPS = 1e-9;
	}
 
	static class Triple implements Comparable<Triple> {
		int x;
		int y;
 
		int z;
 
		Triple(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		@Override
		public int compareTo(Triple o) {
			if (x == o.x && y == o.y)
				return z - o.z;
			if (x == o.x)
				return y - o.y;
			return x - o.x;
		}
 
		@Override
		public String toString() { return "(" + x + ", " + y + ", " + z + ")"; }
	}
 
	static class Pair implements Comparable<Pair> {
		int x;
		int y;
 
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
 
		}
 
		@Override
		public int compareTo(Pair o) {
			if (x == o.x)
				return y - o.y;
			return x - o.x;
		}
 
		@Override
		public String toString() {
 
			return "(" + x + ", " + y + ")";
		}
 
	}
 
	static void shuffle(int[] a) {
		for (int i = 0; i < a.length; i++) {
			int r = i + (int) (Math.random() * (a.length - i));
			int tmp = a[r];
			a[r] = a[i];
			a[i] = tmp;
		}
	}
 
	static int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
 
	static class DSU {
 
		int[] p, rank, setSize;
		int numSets;
 
		DSU(int n) {
			p = new int[n];
			rank = new int[n];
			setSize = new int[n];
			numSets = n;
 
			for (int i = 0; i < n; i++) {
				p[i] = i;
				setSize[i] = 1;
			}
 
		}
 
		int findSet(int n) { return p[n] = p[n] == n ? n : findSet(p[n]); }
 
		boolean isSameSet(int n, int m) { return findSet(n) == findSet(m); }
 
		void mergeSet(int n, int m) {
 
			if (!isSameSet(n, m)) {
				numSets--;
				int p1 = findSet(n);
				int p2 = findSet(m);
 
				if (rank[p1] > rank[p2]) {
					p[p2] = p1;
					setSize[p1] += setSize[p2];
				} else {
					p[p1] = p2;
					setSize[p2] += setSize[p1];
					if (rank[p1] == rank[p2])
						rank[p1]++;
				}
			}
 
		}
 
		int size() { return numSets; }
 
		int setSize(int n) { return setSize[findSet(n)]; }
 
	}
 
	static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;
 
		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
 
		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
 
		public String readLine() throws IOException {
			byte[] buf = new byte[1024];
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}
 
		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do { ret = ret * 10 + c - '0'; } while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
 
		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do { ret = ret * 10 + c - '0'; } while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
 
		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do { ret = ret * 10 + c - '0'; } while ((c = read()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}
 
		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
 
		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}
 
		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
}
