Problem: Walking along a riverside, Mino silently takes a note of something.

"Time," Mino thinks aloud.

"What?"

"Time and tide wait for no man," explains Mino. "My name, taken from the river, always reminds me of this."

"And what are you recording?"

"You see it, tide. Everything has its own period, and I think I've figured out this one," says Mino with confidence.

Doubtfully, Kanno peeks at Mino's records. 

The records are expressed as a string s of characters '0', '1' and '.', where '0' denotes a low tide, '1' denotes a high tide, and '.' denotes an unknown one (either high or low).

You are to help Mino determine whether it's possible that after replacing each '.' independently with '0' or '1', a given integer p is not a period of the resulting string. In case the answer is yes, please also show such a replacement to Mino.

In this problem, a positive integer p is considered a period of string s, if for all 1 ≤ i ≤ \lvert s \rvert - p, the i-th and (i + p)-th characters of s are the same. Here \lvert s \rvert is the length of s.

Input

The first line contains two space-separated integers n and p (1 ≤ p ≤ n ≤ 2000) — the length of the given string and the supposed period, respectively.

The second line contains a string s of n characters — Mino's records. s only contains characters '0', '1' and '.', and contains at least one '.' character.

Output

Output one line — if it's possible that p is not a period of the resulting string, output any one of such strings; otherwise output "No" (without quotes, you can print letters in any case (upper or lower)).

Examples

Input

10 7
1.0.1.0.1.


Output

1000100010


Input

10 6
1.0.1.1000


Output

1001101000


Input

10 9
1........1


Output

No

Note

In the first example, 7 is not a period of the resulting string because the 1-st and 8-th characters of it are different.

In the second example, 6 is not a period of the resulting string because the 4-th and 10-th characters of it are different.

In the third example, 9 is always a period because the only constraint that the first and last characters are the same is already satisfied.

Note that there are multiple acceptable answers for the first two examples, you can print any of them.

Solution (in JAVA):

Solution:


import java.io.*;
import java.nio.charset.Charset;

public class Contest487B {
    public static void main(String[] args) throws FileNotFoundException {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        IOUtil io;
        if (local) {
            io = new IOUtil(new FileInputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest487B.in"), new FileOutputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest487B.out"));
        } else {
            io = new IOUtil(System.in, System.out);
        }

        Task task = new Task(io);
        task.run();
        io.flush();
    }

    public static class Task implements Runnable {
        IOUtil io;

        public Task(IOUtil io) {
            this.io = io;
        }

        @Override
        public void run() {
            int n = io.readInt();
            int p = io.readInt();
            char[] data = new char[n];
            io.readString(data, 0, n);
            boolean possible = false;
            for (int i = 0; i + p < n && !possible; i++) {
                if (data[i] != '.') {
                    if (data[i + p] == '.') {
                        possible = true;
                        data[i + p] = data[i] == '0' ? '1' : '0';
                    } else if (data[i + p] != data[i]) {
                        possible = true;
                    }
                } else {
                    possible = true;
                    data[i] = data[i + p] == '0' ? '1' : '0';
                    if (data[i + p] == '.') {
                        data[i + p] = data[i] == '0' ? '1' : '0';
                    }
                }
            }

            if (!possible) {
                io.write("No");
                return;
            }

            for (int i = 0; i < n; i++) {
                if (data[i] == '.') {
                    data[i] = '0';
                }
            }

            io.write(String.valueOf(data));
        }
    }

    public static class IOUtil {
        private static int BUF_SIZE = 1 << 13;

        private byte[] r_buf = new byte[BUF_SIZE];
        private int r_cur;
        private int r_total;
        private int r_next;
        private final InputStream in;
        private StringBuilder temporary = new StringBuilder();

        StringBuilder w_buf = new StringBuilder();
        private final OutputStream out;

        public IOUtil(InputStream in, OutputStream out) {
            this.in = in;
            this.out = out;
        }

        private void skipBlank() {
            while (r_next <= 32) {
                r_next = read();
            }
        }

        public int readString(char[] data, int offset, int limit) {
            skipBlank();

            int originalLimit = limit;
            while (limit > 0 && r_next > 32) {
                data[offset++] = (char) r_next;
                limit--;
                r_next = read();
            }

            return originalLimit - limit;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (r_next > 32) {
                builder.append((char) r_next);
                r_next = read();
            }

            return builder.toString();
        }

        public String readString() {
            temporary.setLength(0);
            return readString(temporary);
        }

        public long readUnsignedLong() {
            skipBlank();

            long num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 + r_next - '0';
                r_next = read();
            }
            return num;
        }

        public long readLong() {
            skipBlank();

            int sign = 1;
            while (r_next == '+' || r_next == '-') {
                if (r_next == '-') {
                    sign *= -1;
                }
                r_next = read();
            }

            return sign == 1 ? readUnsignedLong() : readNegativeLong();
        }

        public long readNegativeLong() {
            skipBlank();

            long num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 - r_next + '0';
                r_next = read();
            }
            return num;
        }

        public int readUnsignedInt() {
            skipBlank();

            int num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 + r_next - '0';
                r_next = read();
            }
            return num;
        }

        public int readNegativeInt() {
            skipBlank();

            int num = 0;
            while (r_next >= '0' && r_next <= '9') {
                num = num * 10 - r_next + '0';
                r_next = read();
            }
            return num;
        }

        public int readInt() {
            skipBlank();

            int sign = 1;
            while (r_next == '+' || r_next == '-') {
                if (r_next == '-') {
                    sign *= -1;
                }
                r_next = read();
            }

            return sign == 1 ? readUnsignedInt() : readNegativeInt();
        }

        public int read() {
            while (r_total <= r_cur) {
                try {
                    r_total = in.read(r_buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                r_cur = 0;
                if (r_total == -1) {
                    return -1;
                }
            }
            return r_buf[r_cur++];
        }

        public void write(char c) {
            w_buf.append(c);
        }

        public void write(int n) {
            w_buf.append(n);
        }

        public void write(String s) {
            w_buf.append(s);
        }

        public void write(long s) {
            w_buf.append(s);
        }

        public void write(double s) {
            w_buf.append(s);
        }

        public void write(float s) {
            w_buf.append(s);
        }

        public void write(Object s) {
            w_buf.append(s);
        }

        public void write(char[] data, int offset, int cnt) {
            for (int i = offset, until = offset + cnt; i < until; i++) {
                write(data[i]);
            }
        }

        public void flush() {
            try {
                out.write(w_buf.toString().getBytes(Charset.forName("ascii")));
                w_buf.setLength(0);
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public double readDouble() {
            return Double.parseDouble(readString());
        }
    }
}