Problem:
Score : 1000 points

Problem Statement

Takahashi and Aoki are going to together construct a sequence of integers.

First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:

The length of a is N.

Each element in a is an integer between 1 and K, inclusive.

a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.

Then, Aoki will perform the following operation an arbitrary number of times:

Move the first element in a to the end of a.

How many sequences a can be obtained after this procedure, modulo 10^9+7?

Constraints

1≤N≤10^9

1≤K≤10^9

Input

The input is given from Standard Input in the following format:

N K

Output

Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.

Sample Input 1

4 2

Sample Output 1

6

The following six sequences can be obtained:

(1, 1, 1, 1)

(1, 1, 2, 2)

(1, 2, 2, 1)

(2, 2, 1, 1)

(2, 1, 1, 2)

(2, 2, 2, 2)

Sample Input 2

1 10

Sample Output 2

10

Sample Input 3

6 3

Sample Output 3

75

Sample Input 4

1000000000 1000000000

Sample Output 4

875699961

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.util.Random;
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
 * 
 * @author daltao
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "daltao", 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);
            TaskD solver = new TaskD();
            solver.solve(1, in, out);
            out.close();
        }
    }
    static class TaskD {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int k = in.readInt();

            NumberTheory.Modular mod = new NumberTheory.Modular(1e9 + 7);
            NumberTheory.Power pow = new NumberTheory.Power(mod);

            IntList factors = new IntList();
            for (int i = 1; i * i <= n; i++) {
                if (n % i != 0) {
                    continue;
                }
                factors.add(i);
                if (n / i != i) {
                    factors.add(n / i);
                }
            }

            factors.sort();
            IntList cnt = new IntList();
            cnt.expandWith(0, factors.size());

            int ans = 0;
            for (int i = 0; i < factors.size(); i++) {
                int j = factors.get(i);
                int ways = pow.pow(k, DigitUtils.ceilDiv(j, 2));

                for (int t = 0; t < i; t++) {
                    if (j % factors.get(t) == 0) {
                        ways = mod.subtract(ways, cnt.get(t));
                    }
                }

                cnt.set(i, ways);


                if (j % 2 == 0) {
                    ways = mod.mul(ways, j / 2);
                } else {
                    ways = mod.mul(ways, j);
                }
                ans = mod.plus(ways, ans);
            }

            out.println(ans);
        }

    }
    static class IntList {
        private int size;
        private int cap;
        private int[] data;
        private static final int[] EMPTY = new int[0];

        public IntList(int cap) {
            this.cap = cap;
            if (cap == 0) {
                data = EMPTY;
            } else {
                data = new int[cap];
            }
        }

        public IntList(IntList list) {
            this.size = list.size;
            this.cap = list.cap;
            this.data = Arrays.copyOf(list.data, size);
        }

        public IntList() {
            this(0);
        }

        private void ensureSpace(int need) {
            int req = size + need;
            if (req > cap) {
                while (cap < req) {
                    cap = Math.max(cap + 10, 2 * cap);
                }
                data = Arrays.copyOf(data, cap);
            }
        }

        private void checkRange(int i) {
            if (i < 0 || i >= size) {
                throw new ArrayIndexOutOfBoundsException();
            }
        }

        public int get(int i) {
            checkRange(i);
            return data[i];
        }

        public void add(int x) {
            ensureSpace(1);
            data[size++] = x;
        }

        public void expandWith(int x, int len) {
            ensureSpace(len - size);
            while (size < len) {
                add(x);
            }
        }

        public void sort() {
            if (size <= 1) {
                return;
            }
            Randomized.randomizedArray(data, 0, size);
            Arrays.sort(data, 0, size);
        }

        public void set(int i, int x) {
            checkRange(i);
            data[i] = x;
        }

        public int size() {
            return size;
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

        public String toString() {
            return Arrays.toString(toArray());
        }

    }
    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(1 << 20);
        private final Writer os;

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

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

        public FastOutput println(int c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                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);
            }
        }

    }
    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) {
                    throw new RuntimeException(e);
                }
                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 NumberTheory {
        public 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;
            }

        }

        public static class Power {
            final NumberTheory.Modular modular;

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

            public int pow(int x, long n) {
                if (n == 0) {
                    return 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 Randomized {
        static Random random = new Random();

        public static void randomizedArray(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }
    static class DigitUtils {
        private DigitUtils() {}

        public static int floorDiv(int a, int b) {
            return a < 0 ? -ceilDiv(-a, b) : a / b;
        }

        public static int ceilDiv(int a, int b) {
            return a < 0 ? -floorDiv(-a, b) : (a + b - 1) / b;
        }

    }
}