Problem: Surely you have seen insane videos by South Korean rapper PSY, such as "Gangnam Style", "Gentleman" and "Daddy". You might also hear that PSY has been recording video "Oppa Funcan Style" two years ago (unfortunately we couldn't find it on the internet). We will remind you what this hit looked like (you can find original description [here](http://acm.timus.ru/problem.aspx?space=1&num=2107&locale=en)):

On the ground there are n platforms, which are numbered with integers from 1 to n, on i-th platform there is a dancer with number i. Further, every second all the dancers standing on the platform with number i jump to the platform with the number f(i). The moving rule f is selected in advance and is not changed throughout the clip.

The duration of the clip was k seconds and the rule f was chosen in such a way that after k seconds all dancers were in their initial positions (i.e. the i-th dancer stood on the platform with the number i). That allowed to loop the clip and collect even more likes.

PSY knows that enhanced versions of old artworks become more and more popular every day. So he decided to release a remastered-version of his video.

In his case "enhanced version" means even more insanity, so the number of platforms can be up to 10^{18}! But the video director said that if some dancer stays on the same platform all the time, then the viewer will get bored and will turn off the video immediately. Therefore, for all x from 1 to n f(x) ≠ x must hold.

Big part of classic video's success was in that looping, so in the remastered version all dancers should return to their initial positions in the end of the clip as well.

PSY hasn't decided on the exact number of platforms and video duration yet, so he asks you to check if there is a good rule f for different options.

Input

In the first line of input there is one integer t (1 ≤ t ≤ 10^{4}) — the number of options for n and k to check.

In the next t lines the options are given: each option is described with two integers n and k (1 ≤ n ≤ 10^{18}, 1 ≤ k ≤ 10^{15}) — the number of dancers and the duration in seconds.

It is guaranteed that the number of different values of k in one test is not greater than 50.

Output

Print t lines. If the i-th option of the video is feasible, print "YES" (without quotes) in i-th line, otherwise print "NO" (without quotes).

Example

Input

3
7 7
3 8
5 6


Output

YES
NO
YES

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Random;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.util.Collection;
import java.io.IOException;
import java.util.stream.Collectors;
import java.io.UncheckedIOException;
import java.util.Objects;
import java.util.List;
import java.util.stream.Stream;
import java.io.Closeable;
import java.util.Map.Entry;
import java.io.Writer;
import java.util.Comparator;
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);
            FOppaFuncanStyleRemastered solver = new FOppaFuncanStyleRemastered();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class FOppaFuncanStyleRemastered {
        LongPollardRho pollardRho = new LongPollardRho();
        ExtGCD extGCD = new ExtGCD();
        long inf = (long) 1e18;
        LongList collector = new LongList(30000);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int t = in.readInt();
            Query[] queries = new Query[t];
            for (int i = 0; i < t; i++) {
                queries[i] = new Query();
                queries[i].n = in.readLong();
                queries[i].k = in.readLong();
            }
            Map<Long, List<Query>> map = Arrays.stream(queries).collect(Collectors.groupingBy(a -> a.k));
            for (Map.Entry<Long, List<Query>> entry : map.entrySet()) {
                handle(entry.getKey(), entry.getValue());
            }

            for (Query q : queries) {
                out.println(q.ans ? "YES" : "NO");
            }
        }

        public void handle(long k, List<Query> queries) {
            Map<Long, Long> allPrimeFactors = pollardRho.findAllFactors(k, true);
            long[][] pairs = allPrimeFactors.entrySet().stream().map(x -> new long[]{x.getKey(), x.getValue()})
                    .toArray(n -> new long[n][]);

            if (pairs.length == 0) {
                for (Query q : queries) {
                    q.ans = false;
                }
                return;
            }
            if (pairs.length == 1) {
                for (Query q : queries) {
                    q.ans = q.n % pairs[0][0] == 0;
                }
                return;
            }

            if (pairs.length == 2) {
                ILongModular modular = ILongModular.getInstance(pairs[1][0]);
                for (Query q : queries) {
                    long g = extGCD.extgcd(pairs[0][0], pairs[1][0]);
                    if (q.n % g != 0) {
                        q.ans = false;
                        continue;
                    }
                    long x = modular.mul(modular.valueOf(extGCD.getX()), modular.valueOf(q.n));
                    q.ans = !DigitUtils.isMultiplicationOverflow(x, pairs[0][0], q.n);
                }
                return;
            }


            collector.clear();
            for (long[] p : pairs) {
                collector.add(p[0]);
            }
            collector.unique();
            long[] allFactors = collector.getData();
            int m = collector.size();
            int min = (int) allFactors[0];
            //System.err.println(min + "-" + allFactors.length);
            Node[] nodes = new Node[min];
            PairingHeap<Node> heap = PairingHeap.NIL;
            for (int i = 0; i < min; i++) {
                nodes[i] = new Node();
                nodes[i].remain = i;
                nodes[i].dist = i == 0 ? 0 : inf;
                nodes[i].heap = new PairingHeap<>(nodes[i]);
                heap = PairingHeap.merge(heap, nodes[i].heap, Node.sortByDist);
            }
            //TreeSet<Node> set = new TreeSet<>(Node.sortByDist);
            //set.add(nodes[0]);
            while (!PairingHeap.isEmpty(heap)) {
                Node node = PairingHeap.peek(heap);
                heap = PairingHeap.pop(heap, Node.sortByDist);
                for (int i = 0; i < m; i++) {
                    long d = allFactors[i];
                    Node next = nodes[DigitUtils.mod(node.remain + d, min)];
                    if (next.dist <= node.dist + d) {
                        continue;
                    }
                    //set.remove(next);
                    next.dist = node.dist + d;
                    //set.add(next);
                    heap = PairingHeap.decrease(heap, next.heap, next, Node.sortByDist);
                }
            }

            for (Query q : queries) {
                Node node = nodes[DigitUtils.mod(q.n, min)];
                q.ans = node.dist <= q.n;
            }
        }

    }

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

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

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

        public FastOutput println(String c) {
            cache.append(c).append('\n');
            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 interface ILongModular {
        long plus(long a, long b);

        long valueOf(long x);

        long mul(long a, long b);

        static ILongModular getInstance(long mod) {
            return mod <= (1L << 54) ? new LongModularDanger(mod) : new LongModular(mod);
        }

    }

    static class PairingHeap<T> implements Cloneable {
        public static final PairingHeap NIL = new PairingHeap(null);
        PairingHeap<T> father = NIL;
        PairingHeap<T> prev = NIL;
        PairingHeap<T> next = NIL;
        PairingHeap<T> children = NIL;
        private T val;

        static {
            NIL.children = NIL.prev = NIL.next = NIL.children;
        }

        public PairingHeap(T val) {
            this.val = val;
        }

        private static <T> void detach(PairingHeap<T> father, PairingHeap<T> child) {
            if (father == NIL || child == NIL) {
                return;
            }

            child.prev.next = child.next;
            child.next.prev = child.prev;

            if (child.next == child) {
                father.children = NIL;
            } else if (father.children == child) {
                father.children = child.next;
            }
            child.next = child.prev = child.father = NIL;
        }

        private static <T> void attach(PairingHeap<T> father, PairingHeap<T> child) {
            if (father == NIL || child == NIL) {
                return;
            }

            if (father.children == NIL) {
                child.prev = child.next = child;
                child.father = father;
                father.children = child;
                return;
            }
            child.prev = father.children;
            child.next = father.children.next;
            child.prev.next = child;
            child.next.prev = child;
            child.father = father;
        }

        public static <T> PairingHeap<T> merge(PairingHeap<T> a, PairingHeap<T> b, Comparator<T> comp) {
            if (a == NIL) {
                return b;
            }
            if (b == NIL) {
                return a;
            }
            if (comp.compare(a.val, b.val) > 0) {
                PairingHeap<T> tmp = a;
                a = b;
                b = tmp;
            }
            attach(a, b);
            return a;
        }

        public static <T> T peek(PairingHeap<T> root) {
            return root.val;
        }

        public static <T> PairingHeap<T> decrease(PairingHeap<T> root, PairingHeap<T> node,
                                                  T val, Comparator<T> comp) {
            if (root == node) {
                root.val = val;
                return root;
            }
            detach(node.father, node);
            node.val = val;
            return merge(root, node, comp);
        }

        private static <T> PairingHeap<T> popByLoop(PairingHeap<T> head, Comparator<T> comp) {
            PairingHeap<T> loop = head;
            loop.father = NIL;
            loop.father.children = NIL;
            for (PairingHeap<T> i = loop.next; i != loop; i = i.next) {
                loop.father = NIL;
            }

            PairingHeap<T> begin = loop;
            PairingHeap<T> end = begin.prev;
            end.next = NIL;

            while (begin.next != NIL) {
                PairingHeap<T> next = begin.next.next;
                PairingHeap<T> m = merge(begin, begin.next, comp);
                m.next = NIL;
                begin = next;
                if (begin == NIL) {
                    begin = end = m;
                } else {
                    end.next = m;
                    end = m;
                }
            }
            begin.prev = begin.next = NIL;
            return begin;
        }

        public static <T> PairingHeap<T> pop(PairingHeap<T> root, Comparator<T> comp) {
            if (root.children == NIL) {
                return NIL;
            }
            return popByLoop(root.children, comp);
        }

        public static <T> boolean isEmpty(PairingHeap<T> root) {
            return root == NIL;
        }

        public PairingHeap<T> clone() {
            PairingHeap<T> ans = new PairingHeap<>(this.val);
            if (children == NIL) {
                return ans;
            }
            attach(ans, children.clone());
            for (PairingHeap<T> i = children.next; i != children; i = i.next) {
                attach(ans, i.clone());
            }
            return ans;
        }

        public String toString() {
            return Objects.toString(val);
        }

    }

    static class GCDs {
        private GCDs() {
        }

        public static long gcd(long a, long b) {
            return a >= b ? gcd0(a, b) : gcd0(b, a);
        }

        private static long gcd0(long a, long b) {
            return b == 0 ? a : gcd0(b, a % b);
        }

    }

    static class LongPower {
        final ILongModular modular;

        public LongPower(ILongModular modular) {
            this.modular = modular;
        }

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

    }

    static class LongModularDanger implements ILongModular {
        final long m;

        public LongModularDanger(long m) {
            this.m = m;
        }

        public long mul(long a, long b) {
            return DigitUtils.mulMod(a, b, m);
        }

        public long plus(long a, long b) {
            return valueOf(a + b);
        }

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

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static long round(double x) {
            if (x >= 0) {
                return (long) (x + 0.5);
            } else {
                return (long) (x - 0.5);
            }
        }

        public static boolean isMultiplicationOverflow(long a, long b, long limit) {
            if (limit < 0) {
                limit = -limit;
            }
            if (a < 0) {
                a = -a;
            }
            if (b < 0) {
                b = -b;
            }
            if (a == 0 || b == 0) {
                return false;
            }
            //a * b > limit => a > limit / b
            return a > limit / b;
        }

        public static int mod(long x, int mod) {
            x %= mod;
            if (x < 0) {
                x += mod;
            }
            return (int) x;
        }

        public static long mod(long x, long mod) {
            x %= mod;
            if (x < 0) {
                x += mod;
            }
            return x;
        }

        public static long mulMod(long a, long b, long mod) {
            long k = DigitUtils.round((double) a / mod * b);
            return DigitUtils.mod(a * b - k * mod, mod);
        }

    }

    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;
        }

        public long readLong() {
            int sign = 1;

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

            long 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 LongMillerRabin {
        ILongModular modular;
        LongPower power;
        Random random = new Random();

        public boolean mr(long n, int s) {
            if (n <= 1) {
                return false;
            }
            if (n == 2) {
                return true;
            }
            if (n % 2 == 0) {
                return false;
            }
            modular = ILongModular.getInstance(n);
            power = new LongPower(modular);
            for (int i = 0; i < s; i++) {
                long x = (long) (random.nextDouble() * (n - 2) + 2);
                if (!mr0(x, n)) {
                    return false;
                }
            }
            return true;
        }

        private boolean mr0(long x, long n) {
            long exp = n - 1;
            while (true) {
                long y = power.pow(x, exp);
                if (y != 1 && y != n - 1) {
                    return false;
                }
                if (y != 1 || exp % 2 == 1) {
                    break;
                }
                exp = exp / 2;
            }
            return true;
        }

    }

    static class Query {
        long n;
        long k;
        boolean ans;

    }

    static class Randomized {
        static Random random = new Random();

        public static void randomizedArray(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long 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 LongPollardRho {
        LongMillerRabin mr = new LongMillerRabin();
        ILongModular modular;
        Random random = new Random();

        public long findFactor(long n, boolean danger) {
            if (mr.mr(n, 3)) {
                return n;
            }
            modular = ILongModular.getInstance(n);
            while (true) {
                long f = findFactor0((long) (random.nextDouble() * n), (long) (random.nextDouble() * n), n);
                if (f != -1) {
                    return f;
                }
            }
        }

        private long findFactor0(long x, long c, long n) {
            long xi = x;
            long xj = x;
            int j = 2;
            int i = 1;
            while (i < n) {
                i++;
                xi = modular.plus(modular.mul(xi, xi), c);
                long g = GCDs.gcd(n, Math.abs(xi - xj));
                if (g != 1 && g != n) {
                    return g;
                }
                if (i == j) {
                    j = j << 1;
                    xj = xi;
                }
            }
            return -1;
        }

        public Map<Long, Long> findAllFactors(long n, boolean danger) {
            Map<Long, Long> map = new HashMap();
            findAllFactors(map, n, danger);
            return map;
        }

        private void findAllFactors(Map<Long, Long> map, long n, boolean danger) {
            if (n == 1) {
                return;
            }
            long f = findFactor(n, danger);
            if (f == n) {
                Long value = map.get(f);
                if (value == null) {
                    value = 1L;
                }
                map.put(f, value * f);
                return;
            }
            findAllFactors(map, f, danger);
            findAllFactors(map, n / f, danger);
        }

    }

    static class ExtGCD {
        private long x;
        private long y;
        private long g;

        public long getX() {
            return x;
        }

        public long extgcd(long a, long b) {
            if (a >= b) {
                g = extgcd0(a, b);
            } else {
                g = extgcd0(b, a);
                long tmp = x;
                x = y;
                y = tmp;
            }
            return g;
        }

        private long extgcd0(long a, long b) {
            if (b == 0) {
                x = 1;
                y = 0;
                return a;
            }
            long g = extgcd0(b, a % b);
            long n = x;
            long m = y;
            x = m;
            y = n - m * (a / b);
            return g;
        }

    }

    static class Node {
        long dist;
        int remain;
        PairingHeap<Node> heap;
        static Comparator<Node> sortByDist = (a, b) -> a.dist == b.dist ? a.remain - b.remain : Long.compare(a.dist, b.dist);

    }

    static class LongModular implements ILongModular {
        final long m;

        public LongModular(long m) {
            this.m = m;
        }

        public long mul(long a, long b) {
            return b == 0 ? 0 : ((mul(a, b >> 1) << 1) % m + a * (b & 1)) % m;
        }

        public long plus(long a, long b) {
            return valueOf(a + b);
        }

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

    }

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

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

        public long[] getData() {
            return data;
        }

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

        public LongList() {
            this(0);
        }

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

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

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

        public void unique() {
            if (size <= 1) {
                return;
            }

            sort();
            int wpos = 1;
            for (int i = 1; i < size; i++) {
                if (data[i] != data[wpos - 1]) {
                    data[wpos++] = data[i];
                }
            }
            size = wpos;
        }

        public int size() {
            return size;
        }

        public void clear() {
            size = 0;
        }

        public String toString() {
            return Arrays.toString(Arrays.copyOf(data, size));
        }

    }
}