Nazar, a student of the scientific lyceum of the Kingdom of Kremland, is known for his outstanding mathematical abilities. Today a math teacher gave him a very difficult task.

Consider two infinite sets of numbers. The first set consists of odd positive numbers (1, 3, 5, 7, …), and the second set consists of even positive numbers (2, 4, 6, 8, …). At the first stage, the teacher writes the first number on the endless blackboard from the first set, in the second stage — the first two numbers from the second set, on the third stage — the next four numbers from the first set, on the fourth — the next eight numbers from the second set and so on. In other words, at each stage, starting from the second, he writes out two times more numbers than at the previous one, and also changes the set from which these numbers are written out to another. 

The ten first written numbers: 1, 2, 4, 3, 5, 7, 9, 6, 8, 10. Let's number the numbers written, starting with one.

The task is to find the sum of numbers with numbers from l to r for given integers l and r. The answer may be big, so you need to find the remainder of the division by 1000000007 (10^9+7).

Nazar thought about this problem for a long time, but didn't come up with a solution. Help him solve this problem.

Input

The first line contains two integers l and r (1 ≤ l ≤ r ≤ 10^{18}) — the range in which you need to find the sum.

Output

Print a single integer — the answer modulo 1000000007 (10^9+7).

Examples

Input


1 3


Output


7

Input


5 14


Output


105

Input


88005553535 99999999999


Output


761141116

Note

In the first example, the answer is the sum of the first three numbers written out (1 + 2 + 4 = 7).

In the second example, the numbers with numbers from 5 to 14: 5, 7, 9, 6, 8, 10, 12, 14, 16, 18. Their sum is 105.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        CProblemForNazar solver = new CProblemForNazar();
        solver.solve(1, in, out);
        out.close();
    }

    static class CProblemForNazar {
        private static final int MOD = (int) 1e9 + 7;

        public void solve(int testNumber, LightScanner in, LightWriter out) {
            // out.setBoolLabel(LightWriter.BoolLabel.YES_NO_FIRST_UP);
            long l = in.longs(), r = in.longs();
            out.ansln((ans(r) - ans(l - 1) + MOD) % MOD);
        }

        private static long ans(long r) {
            long even = 0, odd = 0;
            long t = r;
            for (int i = 1; i <= 60; i++) {
                long v = (1L << i) - 1;
                if (v > r) {
                    if (i % 2 == 1) {
                        odd += t;
                    } else {
                        even += t;
                    }
                    break;
                }
                long c = (1L << (i - 1));
                t -= c;
                c %= MOD;

                if (i % 2 == 1) {
                    odd += c;
                } else {
                    even += c;
                }
                even %= MOD;
                odd %= MOD;
            }
            even %= MOD;
            odd %= MOD;
            long ans = 0;
            ans += (even + 1L) * even % MOD;
            ans += odd * odd % MOD;
            ans %= MOD;
            return ans;
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public long longs() {
            return Long.parseLong(string());
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ansln(long... n) {
            for (long n1 : n) {
                ans(n1).ln();
            }
            return this;
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }
}

