Problem: The Travelling Salesman spends a lot of time travelling so he tends to get bored. To pass time, he likes to perform operations on numbers. One such operation is to take a positive integer x and reduce it to the number of bits set to 1 in the binary representation of x. For example for number 13 it's true that 1310 = 11012, so it has 3 bits set and 13 will be reduced to 3 in one operation.

He calls a number special if the minimum number of operations to reduce it to 1 is k.

He wants to find out how many special numbers exist which are not greater than n. Please help the Travelling Salesman, as he is about to reach his destination!

Since the answer can be large, output it modulo 109 + 7.

Input

The first line contains integer n (1 ≤ n < 21000).

The second line contains integer k (0 ≤ k ≤ 1000).

Note that n is given in its binary representation without any leading zeros.

Output

Output a single integer — the number of special numbers not greater than n, modulo 109 + 7.

Examples

Input

110
2


Output

3


Input

111111011
2


Output

169

Note

In the first sample, the three special numbers are 3, 5 and 6. They get reduced to 2 in one operation (since there are two set bits in each of 3, 5 and 6) and then to 1 in one more operation (since there is only one set bit in 2).

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
 
public class Main1 {
	static PrintWriter out = new PrintWriter(System.out, true);
	static FastReader input = new FastReader();
	static char[] x;
	static int n, k, a[], MOD = (int) (1e9) + 7;
	static long memo[][][];
	static boolean v[][][];
 
	static int countBits(int x) {
		int cnt = 0;
		for (int i = 0; i < 32; i++) {
			int t = 1 << i;
			if ((t & x) != 0)
				cnt++;
		}
		return cnt;
	}
 
	static long solve(int i, int bits, int t) {
		if (i >= n) {
			int tmpk = 1;
			if (bits==0) return 0;
			int x = bits;
			while (x > 1) {
				x = countBits(x);
				tmpk++;
			}
 
			if (tmpk == k)
				return 1;
 
			return 0;
 
		}
		if (v[i][bits][t]) {
			return memo[i][bits][t];
		}
		v[i][bits][t] = true;
		long sum = 0;
		if (a[i] == 1) {
			sum += solve(i + 1, bits, 1);
			sum += solve(i + 1, bits + 1, t);
		}
		if (a[i] == 0) {
			sum += solve(i + 1, bits, t);
			if (t == 1)
				sum += solve(i + 1, bits + 1, t);
		}
		return memo[i][bits][t] = sum % MOD;
	}
 
	public static void main(String[] args) throws IOException {
		x = input.nextLine().toCharArray();
		n = x.length;
		a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = x[i] == '1' ? 1 : 0;
		k = input.nextInt();
		memo = new long[n + 1][1001][2];
		v = new boolean[n + 1][1001][2];
		if (k == 0 && (a[n - 1] == 1 || a.length > 1)) {
			out.println(1);
		} else {
			long ans = solve(0, 0, 0);
			if (k == 1 && (a[n - 1] == 1 || a.length > 1)) {
				ans--;
			}
			out.println((MOD + ans) % MOD);
		}
 
	}
 
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader() {
			// try {
			// br = new BufferedReader(new FileReader(new File("overcode.in")));
			// } 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();
		}
	}
}