ZS the Coder has a large tree. It can be represented as an undirected connected graph of n vertices numbered from 0 to n - 1 and n - 1 edges between them. There is a single nonzero digit written on each edge.

One day, ZS the Coder was bored and decided to investigate some properties of the tree. He chose a positive integer M, which is coprime to 10, i.e. <image>.

ZS consider an ordered pair of distinct vertices (u, v) interesting when if he would follow the shortest path from vertex u to vertex v and write down all the digits he encounters on his path in the same order, he will get a decimal representaion of an integer divisible by M.

Formally, ZS consider an ordered pair of distinct vertices (u, v) interesting if the following states true:

  * Let a1 = u, a2, ..., ak = v be the sequence of vertices on the shortest path from u to v in the order of encountering them; 
  * Let di (1 ≤ i < k) be the digit written on the edge between vertices ai and ai + 1; 
  * The integer <image> is divisible by M. 



Help ZS the Coder find the number of interesting pairs!

Input

The first line of the input contains two integers, n and M (2 ≤ n ≤ 100 000, 1 ≤ M ≤ 109, <image>) — the number of vertices and the number ZS has chosen respectively.

The next n - 1 lines contain three integers each. i-th of them contains ui, vi and wi, denoting an edge between vertices ui and vi with digit wi written on it (0 ≤ ui, vi < n, 1 ≤ wi ≤ 9).

Output

Print a single integer — the number of interesting (by ZS the Coder's consideration) pairs.

Examples

Input

6 7
0 1 2
4 2 4
2 0 1
3 0 9
2 5 7


Output

7


Input

5 11
1 2 3
2 0 3
3 0 3
4 3 3


Output

8

Note

In the first sample case, the interesting pairs are (0, 4), (1, 2), (1, 5), (3, 2), (2, 5), (5, 2), (3, 5). The numbers that are formed by these pairs are 14, 21, 217, 91, 7, 7, 917 respectively, which are all multiples of 7. Note that (2, 5) and (5, 2) are considered different. 

<image>

In the second sample case, the interesting pairs are (4, 0), (0, 4), (3, 2), (2, 3), (0, 1), (1, 0), (4, 1), (1, 4), and 6 of these pairs give the number 33 while 2 of them give the number 3333, which are all multiples of 11.

<image>
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.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
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 << 29);
        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);
            CDigitTree solver = new CDigitTree();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class CDigitTree {
        Modular mod;
        int[] pow;
        int[] inv;
        long cnt = 0;
        IntegerHashMap hm = new IntegerHashMap((int) 1e6, false);
        List<Node> trace = new ArrayList<>((int) 1e5);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int m = in.readInt();
            mod = new Modular(m);
            pow = new int[n + 1];
            inv = new int[n + 1];
            pow[0] = inv[0] = 1;
            pow[1] = mod.valueOf(10);
            inv[1] = new Power(mod).inverse(pow[1]);
            for (int i = 2; i <= n; i++) {
                pow[i] = mod.mul(pow[i - 1], pow[1]);
                inv[i] = mod.mul(inv[i - 1], inv[1]);
            }


            Node[] nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
                nodes[i].id = i;
            }

            for (int i = 0; i < n - 1; i++) {
                Node a = nodes[in.readInt()];
                Node b = nodes[in.readInt()];
                Edge e = new Edge();
                e.a = a;
                e.b = b;
                e.digit = in.readInt();
                a.adj.add(e);
                b.adj.add(e);
            }

            dac(nodes[0]);
            out.println(cnt);
        }

        public void findSize(Node root, Edge p) {
            root.size = 1;
            for (Edge e : root.adj) {
                if (e == p) {
                    continue;
                }
                Node node = e.other(root);
                findSize(node, e);
                root.size += node.size;
            }
        }

        public Node findCentroid(Node root, Edge p, int total) {
            int max = total - root.size;
            for (Edge e : root.adj) {
                if (e == p) {
                    continue;
                }
                Node node = e.other(root);
                Node ans = findCentroid(node, e, total);
                if (ans != null) {
                    return ans;
                }
                max = Math.max(max, node.size);
            }
            if (max * 2 <= total) {
                return root;
            }
            return null;
        }

        public void trace(Node root, Edge p) {
            Node top = p.other(root);
            root.depth = top.depth + 1;
            root.down = mod.mul(top.down, 10);
            root.down = mod.plus(root.down, p.digit);
            root.up = mod.mul(p.digit, pow[root.depth - 1]);
            root.up = mod.plus(root.up, top.up);

            trace.add(root);
            for (Edge e : root.adj) {
                if (e == p) {
                    continue;
                }
                Node node = e.other(root);
                trace(node, e);
            }
        }

        public void dac(Node root) {
            if (root.adj.isEmpty()) {
                return;
            }
            findSize(root, null);
            root = findCentroid(root, null, root.size);
            root.up = root.down = 0;
            root.depth = 0;
            hm.clear();
            hm.put(root.up, 1);
            for (Edge e : root.adj) {
                trace.clear();
                trace(e.other(root), e);
                //sort then map
                for (Node node : trace) {
                    node.down = mod.mul(node.down, inv[node.depth]);
                    cnt += hm.getOrDefault(mod.valueOf(-node.down), 0);
                }
                for (Node node : trace) {
                    hm.put(node.up, hm.getOrDefault(node.up, 0) + 1);
                }
            }

            SequenceUtils.reverse(root.adj);
            hm.clear();
            for (Edge e : root.adj) {
                trace.clear();
                trace(e.other(root), e);
                //sort then map
                for (Node node : trace) {
                    node.down = mod.mul(node.down, inv[node.depth]);
                    cnt += hm.getOrDefault(mod.valueOf(-node.down), 0);
                }
                for (Node node : trace) {
                    hm.put(node.up, hm.getOrDefault(node.up, 0) + 1);
                }
            }
            cnt += hm.getOrDefault(mod.valueOf(-root.down), 0);

            for (Edge e : root.adj) {
                Node node = e.other(root);
                node.adj.remove(e);
                dac(node);
            }
        }

    }

    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 interface IntegerEntryIterator {
        boolean hasNext();

        void next();

        int getEntryKey();

        int getEntryValue();

    }

    static class IntegerHashMap {
        private int now;
        private int[] slot;
        private int[] version;
        private int[] next;
        private int[] keys;
        private int[] values;
        private int alloc;
        private boolean[] removed;
        private int mask;
        private int size;
        private boolean rehash;
        private Hasher hasher = new Hasher();

        public IntegerHashMap(int cap, boolean rehash) {
            now = 1;
            this.mask = (1 << (32 - Integer.numberOfLeadingZeros(cap - 1))) - 1;
            slot = new int[mask + 1];
            version = new int[slot.length];
            next = new int[cap + 1];
            keys = new int[cap + 1];
            values = new int[cap + 1];
            removed = new boolean[cap + 1];
            this.rehash = rehash;
        }

        private void doubleCapacity() {
            int newSize = Math.max(next.length + 10, next.length * 2);
            next = Arrays.copyOf(next, newSize);
            keys = Arrays.copyOf(keys, newSize);
            values = Arrays.copyOf(values, newSize);
            removed = Arrays.copyOf(removed, newSize);
        }

        public void alloc() {
            alloc++;
            if (alloc >= next.length) {
                doubleCapacity();
            }
            next[alloc] = 0;
            removed[alloc] = false;
            size++;
        }

        private void rehash() {
            int[] newSlots = new int[Math.max(16, slot.length * 2)];
            int[] newVersions = new int[newSlots.length];
            int newMask = newSlots.length - 1;
            for (int i = 0; i < slot.length; i++) {
                access(i);
                if (slot[i] == 0) {
                    continue;
                }
                int head = slot[i];
                while (head != 0) {
                    int n = next[head];
                    int s = hash(keys[head]) & newMask;
                    next[head] = newSlots[s];
                    newSlots[s] = head;
                    head = n;
                }
            }
            this.slot = newSlots;
            this.version = newVersions;
            now = 0;
            this.mask = newMask;
        }

        private int hash(int x) {
            return hasher.hash(x);
        }

        public void put(int x, int y) {
            put(x, y, true);
        }

        public void put(int x, int y, boolean cover) {
            int h = hash(x);
            int s = h & mask;
            access(s);
            if (slot[s] == 0) {
                alloc();
                slot[s] = alloc;
                keys[alloc] = x;
                values[alloc] = y;
            } else {
                int index = findIndexOrLastEntry(s, x);
                if (keys[index] != x) {
                    alloc();
                    next[index] = alloc;
                    keys[alloc] = x;
                    values[alloc] = y;
                } else if (cover) {
                    values[index] = y;
                }
            }
            if (rehash && size >= slot.length) {
                rehash();
            }
        }

        public int getOrDefault(int x, int def) {
            int h = hash(x);
            int s = h & mask;
            access(s);
            if (slot[s] == 0) {
                return def;
            }
            int index = findIndexOrLastEntry(s, x);
            return keys[index] == x ? values[index] : def;
        }

        private int findIndexOrLastEntry(int s, int x) {
            int iter = slot[s];
            while (keys[iter] != x) {
                if (next[iter] != 0) {
                    iter = next[iter];
                } else {
                    return iter;
                }
            }
            return iter;
        }

        public void clear() {
            alloc = 0;
            size = 0;
            now++;
        }

        private void access(int i) {
            if (version[i] != now) {
                version[i] = now;
                slot[i] = 0;
            }
        }

        public IntegerEntryIterator iterator() {
            return new IntegerEntryIterator() {
                int index = 1;
                int readIndex = -1;


                public boolean hasNext() {
                    while (index <= alloc && removed[index]) {
                        index++;
                    }
                    return index <= alloc;
                }


                public int getEntryKey() {
                    return keys[readIndex];
                }


                public int getEntryValue() {
                    return values[readIndex];
                }


                public void next() {
                    if (!hasNext()) {
                        throw new IllegalStateException();
                    }
                    readIndex = index;
                    index++;
                }
            };
        }

        public String toString() {
            IntegerEntryIterator iterator = iterator();
            StringBuilder builder = new StringBuilder("{");
            while (iterator.hasNext()) {
                iterator.next();
                builder.append(iterator.getEntryKey()).append("->").append(iterator.getEntryValue()).append(',');
            }
            if (builder.charAt(builder.length() - 1) == ',') {
                builder.setLength(builder.length() - 1);
            }
            builder.append('}');
            return builder.toString();
        }

    }

    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(long c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(long 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 ExtGCD {
        public static int extGCD(int a, int b, int[] xy) {
            if (a >= b) {
                return extGCD0(a, b, xy);
            }
            int ans = extGCD0(b, a, xy);
            SequenceUtils.swap(xy, 0, 1);
            return ans;
        }

        private static int extGCD0(int a, int b, int[] xy) {
            if (b == 0) {
                xy[0] = 1;
                xy[1] = 0;
                return a;
            }
            int ans = extGCD0(b, a % b, xy);
            int x = xy[0];
            int y = xy[1];
            xy[0] = y;
            xy[1] = x - a / b * y;
            return ans;
        }

    }

    static class Node {
        int id;
        List<Edge> adj = new ArrayList<>();
        int size;
        int up;
        int down;
        int depth;

        public String toString() {
            return "" + (id);
        }

    }

    static class Modular {
        int m;

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

    }

    static interface InverseNumber {
    }

    static class SequenceUtils {
        public static void swap(int[] data, int i, int j) {
            int tmp = data[i];
            data[i] = data[j];
            data[j] = tmp;
        }

        public static <T> void swap(List<T> data, int i, int j) {
            T tmp = data.get(i);
            data.set(i, data.get(j));
            data.set(j, tmp);
        }

        public static <T> void reverse(List<T> data, int l, int r) {
            while (l < r) {
                swap(data, l, r);
                l++;
                r--;
            }
        }

        public static <T> void reverse(List<T> data) {
            reverse(data, 0, data.size() - 1);
        }

    }

    static class Hasher {
        private long time = System.nanoTime() + System.currentTimeMillis() * 31L;

        public int shuffle(long z) {
            z += time;
            z = (z ^ (z >>> 33)) * 0x62a9d9ed799705f5L;
            return (int) (((z ^ (z >>> 28)) * 0xcb24d0a5c88c35b3L) >>> 32);
        }

        public int hash(int x) {
            return shuffle(x);
        }

    }

    static class Edge {
        Node a;
        Node b;
        int digit;

        Node other(Node x) {
            return a == x ? b : a;
        }

    }

    static class Power implements InverseNumber {
        static IntExtGCDObject extGCD = new IntExtGCDObject();
        final Modular modular;

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

        public int inverse(int x) {
            int ans = inverseExtGCD(x);
//        if(modular.mul(ans, x) != 1){
//            throw new IllegalStateException();
//        }
            return ans;
        }

        public int inverseExtGCD(int x) {
            if (extGCD.extgcd(x, modular.getMod()) != 1) {
                throw new IllegalArgumentException();
            }
            return modular.valueOf(extGCD.getX());
        }

    }

    static class IntExtGCDObject {
        private int[] xy = new int[2];

        public int extgcd(int a, int b) {
            return ExtGCD.extGCD(a, b, xy);
        }

        public int getX() {
            return xy[0];
        }

    }
}

