Snuke has a string x of length N. Initially, every character in x is `0`.

Snuke can do the following two operations any number of times in any order:

* Choose A consecutive characters in x and replace each of them with `0`.
* Choose B consecutive characters in x and replace each of them with `1`.



Find the number of different strings that x can be after Snuke finishes doing operations. This count can be enormous, so compute it modulo (10^9+7).

Constraints

* 1 \leq N \leq 5000
* 1 \leq A,B \leq N
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N A B


Output

Print the number of different strings that x can be after Snuke finishes doing operations, modulo (10^9+7).

Examples

Input

4 2 3


Output

11


Input

10 7 2


Output

533


Input

1000 100 10


Output

828178524
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            CRangeSet solver = new CRangeSet();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class CRangeSet {
        Debug debug = new Debug(false);
        Modular mod = new Modular(1e9 + 7);
        Power pow = new Power(mod);
        int a;
        int b;
        int[] f;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            a = in.readInt();
            b = in.readInt();
            if (a < b) {
                int tmp = a;
                a = b;
                b = tmp;
            }

            f = new int[a];
            SequenceUtils.deepFill(f, -1);

//        for (int i = 0; i < a; i++) {
//            debug.debug("f(" + i + ")", f(i));
//        }

            ArrayIndex ai = new ArrayIndex(n + 1, a, 2);
            int[] dp = new int[ai.totalSize()];
            dp[ai.indexOf(0, 0, 0)] = 1;
            dp[ai.indexOf(0, 0, 1)] = 1;
            int[] sum = new int[2];
            for (int i = 1; i <= n; i++) {
                Arrays.fill(sum, 0);
                for (int j = 0; j < a; j++) {
                    int lend = j == i - 1 ? 1 : 0;
                    sum[0] = mod.plus(sum[0], mod.mul(dp[ai.indexOf(i - 1, j, 0)], f(j - 2 + lend)));
                }
                for (int j = 0; j < b; j++) {
                    sum[1] = mod.plus(sum[1], dp[ai.indexOf(i - 1, j, 1)]);
                }
                debug.debug("i", i - 1);
                debug.debug("sum", sum);
                for (int k = 1; k < a; k++) {
                    if (k == 1) {
                        dp[ai.indexOf(i, k, 0)] = sum[1];
                    } else {
                        dp[ai.indexOf(i, k, 0)] = dp[ai.indexOf(i - 1, k - 1, 0)];
                    }
                }
                for (int k = 1; k < b; k++) {
                    if (k == 1) {
                        dp[ai.indexOf(i, k, 1)] = sum[0];
                    } else {
                        dp[ai.indexOf(i, k, 1)] = dp[ai.indexOf(i - 1, k - 1, 1)];
                    }
                }
            }

            Arrays.fill(sum, 0);
            for (int j = 0; j < a; j++) {
                sum[0] = mod.plus(sum[0], mod.mul(dp[ai.indexOf(n, j, 0)], f(j - 1)));
            }
            for (int j = 0; j < b; j++) {
                sum[1] = mod.plus(sum[1], dp[ai.indexOf(n, j, 1)]);
            }
            debug.debug("sum", sum);

            int invalid = mod.plus(sum[0], sum[1]);
            int total = pow.pow(2, n);
            int valid = mod.subtract(total, invalid);
            out.println(valid);
        }

        public int f(int i) {
            if (i <= 0) {
                return 1;
            }
            if (f[i] == -1) {
                f[i] = f(i - 1);
                for (int t = b; i - t >= 0; t++) {
                    f[i] = mod.plus(f[i], f(i - t - 1));
                }
            }
            return f[i];
        }

    }

    static class Power implements InverseNumber {
        final Modular modular;

        public Power(Modular modular) {
            this.modular = modular;
        }

        public int pow(int x, int n) {
            if (n == 0) {
                return modular.valueOf(1);
            }
            long r = pow(x, n >> 1);
            r = modular.valueOf(r * r);
            if ((n & 1) == 1) {
                r = modular.valueOf(r * x);
            }
            return (int) r;
        }

    }

    static class Modular {
        int m;

        public Modular(int m) {
            this.m = m;
        }

        public Modular(long m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public Modular(double m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public int subtract(int x, int y) {
            return valueOf(x - y);
        }

        public String toString() {
            return "mod " + m;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, int x) {
            if (offline) {
                debug(name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf("%s=%s", name, x);
                out.println();
            }
            return this;
        }

        public Debug debug(String name, Object x) {
            return debug(name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass().isArray()) {
                    out.append(name);
                    for (int i : indexes) {
                        out.printf("[%d]", i);
                    }
                    out.append("=").append("" + x);
                    out.println();
                } else {
                    indexes = Arrays.copyOf(indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class SequenceUtils {
        public static void deepFill(Object array, int val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof int[]) {
                int[] intArray = (int[]) array;
                Arrays.fill(intArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFill(obj, val);
                }
            }
        }

    }

    static interface InverseNumber {
    }

    static class ArrayIndex {
        int[] dimensions;

        public ArrayIndex(int... dimensions) {
            this.dimensions = dimensions;
        }

        public int totalSize() {
            int ans = 1;
            for (int x : dimensions) {
                ans *= x;
            }
            return ans;
        }

        public int indexOf(int a, int b) {
            return a * dimensions[1] + b;
        }

        public int indexOf(int a, int b, int c) {
            return indexOf(a, b) * dimensions[2] + c;
        }

    }
}

