Problem: Lunar New Year is approaching, and Bob received a gift from his friend recently — a recursive sequence! He loves this sequence very much and wants to play with it.

Let f_1, f_2, …, f_i, … be an infinite sequence of positive integers. Bob knows that for i > k, f_i can be obtained by the following recursive equation:

$$$f_i = \left(f_{i - 1} ^ {b_1} ⋅ f_{i - 2} ^ {b_2} ⋅ ⋅⋅⋅ ⋅ f_{i - k} ^ {b_k}\right) mod p,$$$

which in short is

$$$f_i = \left(∏_{j = 1}^{k} f_{i - j}^{b_j}\right) mod p,$$$

where p = 998 244 353 (a widely-used prime), b_1, b_2, …, b_k are known integer constants, and x mod y denotes the remainder of x divided by y.

Bob lost the values of f_1, f_2, …, f_k, which is extremely troublesome – these are the basis of the sequence! Luckily, Bob remembers the first k - 1 elements of the sequence: f_1 = f_2 = … = f_{k - 1} = 1 and the n-th element: f_n = m. Please find any possible value of f_k. If no solution exists, just tell Bob that it is impossible to recover his favorite sequence, regardless of Bob's sadness.

Input

The first line contains a positive integer k (1 ≤ k ≤ 100), denoting the length of the sequence b_1, b_2, …, b_k.

The second line contains k positive integers b_1, b_2, …, b_k (1 ≤ b_i < p).

The third line contains two positive integers n and m (k < n ≤ 10^9, 1 ≤ m < p), which implies f_n = m.

Output

Output a possible value of f_k, where f_k is a positive integer satisfying 1 ≤ f_k < p. If there are multiple answers, print any of them. If no such f_k makes f_n = m, output -1 instead.

It is easy to show that if there are some possible values of f_k, there must be at least one satisfying 1 ≤ f_k < p.

Examples

Input


3
2 3 5
4 16


Output


4


Input


5
4 7 1 5 6
7 14187219


Output


6


Input


8
2 3 5 6 1 7 9 10
23333 1


Output


1


Input


1
2
88888 66666


Output


-1


Input


3
998244352 998244352 998244352
4 2


Output


-1


Input


10
283 463 213 777 346 201 463 283 102 999
2333333 6263423


Output


382480067

Note

In the first sample, we have f_4 = f_3^2 ⋅ f_2^3 ⋅ f_1^5. Therefore, applying f_3 = 4, we have f_4 = 16. Note that there can be multiple answers.

In the third sample, applying f_7 = 1 makes f_{23333} = 1.

In the fourth sample, no such f_1 makes f_{88888} = 66666. Therefore, we output -1 instead.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Random;
import java.util.Deque;
import java.util.function.Supplier;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.util.Collection;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.util.function.Consumer;
import java.util.stream.Stream;
import java.io.Closeable;
import java.io.Writer;
import java.util.ArrayDeque;
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);
            TaskF solver = new TaskF();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class TaskF {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            Modular mod = new Modular(998244353);
            int k = in.readInt();
            int[] b = new int[k];
            for (int i = 0; i < k; i++) {
                b[i] = in.readInt();
            }
            int n = in.readInt();
            int m = in.readInt();

            IntList coes = new IntList();
            coes.addAll(b);
            IntList a = new IntList();
            a.expandWith(0, k);
            a.set(k - 1, 1);
            LinearRecurrenceSolver solver = LinearRecurrenceSolver
                    .newSolverFromLinearRecurrence(coes, mod.getModularForPowerComputation());
            int t = solver.solve(n - 1, a);
            ModPrimeRoot root = new ModPrimeRoot(mod);
            int ans = root.root(m, t);
            out.println(ans);
        }

    }

    static class Buffer<T> {
        private Deque<T> deque;
        private Supplier<T> supplier;
        private Consumer<T> cleaner;

        public Buffer(Supplier<T> supplier) {
            this(supplier, (x) -> {
            });
        }

        public Buffer(Supplier<T> supplier, Consumer<T> cleaner) {
            this(supplier, cleaner, 0);
        }

        public Buffer(Supplier<T> supplier, Consumer<T> cleaner, int exp) {
            this.supplier = supplier;
            this.cleaner = cleaner;
            deque = new ArrayDeque<>(exp);
        }

        public T alloc() {
            return deque.isEmpty() ? supplier.get() : deque.removeFirst();
        }

        public void release(T e) {
            cleaner.accept(e);
            deque.addLast(e);
        }

    }

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

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

        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);
        }

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

        public void addAll(int[] x) {
            addAll(x, 0, x.length);
        }

        public void addAll(int[] x, int offset, int len) {
            ensureSpace(size + len);
            System.arraycopy(x, offset, data, size, len);
            size += len;
        }

        public void addAll(IntList list) {
            addAll(list.data, 0, list.size);
        }

        public void expandWith(int x, int len) {
            ensureSpace(len);
            while (size < len) {
                data[size++] = x;
            }
        }

        public void retain(int n) {
            if (n < 0) {
                throw new IllegalArgumentException();
            }
            if (n >= size) {
                return;
            }
            size = n;
        }

        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 void clear() {
            size = 0;
        }

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

        public boolean equals(Object obj) {
            if (!(obj instanceof IntList)) {
                return false;
            }
            IntList other = (IntList) obj;
            return SequenceUtils.equal(data, 0, size - 1, other.data, 0, other.size - 1);
        }

        public int hashCode() {
            int h = 1;
            for (int i = 0; i < size; i++) {
                h = h * 31 + data[i];
            }
            return h;
        }

    }

    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 ModPrimeRoot {
        private RelativePrimeModLog log;
        private Modular mod;
        private Modular powMod;
        private static ExtGCD extGCD = new ExtGCD();
        private Power power;
        private int primitiveRoot;

        public ModPrimeRoot(Modular p) {
            this(p, new PrimitiveRoot(p).findMinPrimitiveRoot());
        }

        public ModPrimeRoot(Modular p, int g) {
            mod = p;
            log = new RelativePrimeModLog(g, mod);
            powMod = mod.getModularForPowerComputation();
            power = new Power(mod);
            primitiveRoot = g;
        }

        public int root(int x, int k) {
            x = mod.valueOf(x);
            k = powMod.valueOf(k);
            if (x == 0) {
                if (k == 0) {
                    return -1;
                }
                return 0;
            }
            if (k == 0) {
                if (x == 1) {
                    return 1;
                }
                return -1;
            }

            int logx = log.log(x);
            int gcd = (int) extGCD.extgcd(k, powMod.getMod());
            if (logx % gcd != 0) {
                return -1;
            }
            int loga = powMod.mul(logx / gcd, powMod.valueOf(extGCD.getX()));
            return power.pow(primitiveRoot, loga);
        }

    }

    static class IntHashMap {
        private int[] slot;
        private int[] next;
        private int[] keys;
        private int[] values;
        private int alloc;
        private boolean[] removed;
        private int mask;
        private int size;
        private boolean rehash;

        public IntHashMap(int cap, boolean rehash) {
            this.mask = (1 << (32 - Integer.numberOfLeadingZeros(cap - 1))) - 1;
            slot = new int[mask + 1];
            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 newMask = newSlots.length - 1;
            for (int i = 0; i < slot.length; 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.mask = newMask;
        }

        private int hash(int x) {
            return x ^ (x >>> 16);
        }

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

        public void put(int x, int y, boolean cover) {
            int h = hash(x);
            int s = h & mask;
            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;
            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 IntEntryIterator iterator() {
            return new IntEntryIterator() {
                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() {
            IntEntryIterator 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 Gcd {
        public int gcd(int a, int b) {
            return a >= b ? gcd0(a, b) : gcd0(b, a);
        }

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

    }

    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);
            }
        }

    }

    static class RelativePrimeModLog {
        Modular mod;
        Modular powMod;
        int x;
        int invX;
        int phi;
        IntHashMap map;
        int m;
        CachedPow pow;
        private static ExtGCD extGCD = new ExtGCD();

        public RelativePrimeModLog(int x, Modular mod) {
            this.x = x;
            this.mod = mod;
            phi = mod.getMod();
            powMod = new Modular(phi);
            if (extGCD.extgcd(x, mod.getMod()) != 1) {
                throw new IllegalArgumentException();
            }
            invX = mod.valueOf(extGCD.getX());
            pow = new CachedPow(invX, mod);

            m = (int) Math.ceil(Math.sqrt(phi));
            map = new IntHashMap(m, false);

            int prod = mod.valueOf(1);
            for (int i = 0; i < m; i++) {
                map.putIfNotExist(prod, i);
                prod = mod.mul(prod, x);
            }
        }

        public int log(int y) {
            y = mod.valueOf(y);
            int start = 0;
            while (start * m < phi) {
                int inverse = pow.pow(powMod.valueOf(start * m));
                int val = map.getOrDefault(mod.mul(inverse, y), -1);
                if (val >= 0) {
                    return powMod.valueOf(val + start * m);
                }
                start++;
            }
            return -1;
        }

    }

    static class LinearRecurrenceSolver {
        Modular mod;
        IntList coe;
        IntList p;
        IntList remainder;
        Power pow;
        int n;

        private LinearRecurrenceSolver(IntList coe, Modular mod) {
            this.coe = coe;
            this.mod = mod;
            n = coe.size();
            pow = new Power(mod);
            remainder = new IntList(coe.size());
            p = new IntList(coe.size() + 1);
            for (int i = n - 1; i >= 0; i--) {
                p.add(mod.valueOf(-coe.get(i)));
            }
            p.add(1);
        }

        public static LinearRecurrenceSolver newSolverFromLinearRecurrence(IntList coe, Modular mod) {
            return new LinearRecurrenceSolver(coe, mod);
        }

        private int solve(IntList a) {
            int ans = 0;
            remainder.expandWith(0, n);
            for (int i = 0; i < n; i++) {
                ans = mod.plus(ans, mod.mul(remainder.get(i), a.get(i)));
            }
            return ans;
        }

        public int solve(long k, IntList a) {
            if (k < a.size()) {
                return a.get((int) k);
            }
            Polynomials.module(k, p, remainder, pow);
            return solve(a);
        }

    }

    static class SequenceUtils {
        public static boolean equal(int[] a, int al, int ar, int[] b, int bl, int br) {
            if ((ar - al) != (br - bl)) {
                return false;
            }
            for (int i = al, j = bl; i <= ar; i++, j++) {
                if (a[i] != b[j]) {
                    return false;
                }
            }
            return true;
        }

    }

    static class PrimitiveRoot {
        private int[] factors;
        private Modular mod;
        private Power pow;
        int phi;
        private static PollardRho rho = new PollardRho();

        public PrimitiveRoot(Modular x) {
            phi = x.getMod() - 1;
            mod = x;
            pow = new Power(mod);
            factors = rho.findAllFactors(phi).keySet().stream().mapToInt(Integer::intValue).toArray();
        }

        public PrimitiveRoot(int x) {
            this(new Modular(x));
        }

        public int findMinPrimitiveRoot() {
            return findMinPrimitiveRoot(2);
        }

        public int findMinPrimitiveRoot(int since) {
            for (int i = since; i < mod.m; i++) {
                boolean flag = true;
                for (int f : factors) {
                    if (pow.pow(i, phi / f) == 1) {
                        flag = false;
                        break;
                    }
                }
                if (flag) {
                    return i;
                }
            }
            return -1;
        }

    }

    static class CachedPow {
        private int[] first;
        private int[] second;
        private Modular mod;

        public CachedPow(int x, Modular mod) {
            this(x, mod.getMod(), mod);
        }

        public CachedPow(int x, int maxExp, Modular mod) {
            this.mod = mod;
            int k = Math.max(1, (int) DigitUtils.round(Math.sqrt(maxExp)));
            first = new int[k];
            second = new int[maxExp / k + 1];
            first[0] = 1;
            for (int i = 1; i < k; i++) {
                first[i] = mod.mul(x, first[i - 1]);
            }
            second[0] = 1;
            int step = mod.mul(x, first[k - 1]);
            for (int i = 1; i < second.length; i++) {
                second[i] = mod.mul(second[i - 1], step);
            }
        }

        public int pow(int exp) {
            return mod.mul(first[exp % first.length], second[exp / first.length]);
        }

    }

    static class MillerRabin {
        Modular modular;
        Power power;
        Random random = new Random();

        public boolean mr(int n, int s) {
            if (n == 2) {
                return true;
            }
            if (n % 2 == 0) {
                return false;
            }
            modular = new Modular(n);
            power = new Power(modular);
            for (int i = 0; i < s; i++) {
                int x = random.nextInt(n - 2) + 2;
                if (!mr0(x, n)) {
                    return false;
                }
            }
            return true;
        }

        private boolean mr0(int x, int n) {
            int exp = n - 1;
            while (true) {
                int 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 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(int 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 class Polynomials {
        public static Buffer<IntList> listBuffer = new Buffer<>(IntList::new, list -> list.clear());
        private static ExtGCD extGCD = new ExtGCD();

        public static int rankOf(IntList p) {
            int[] data = p.getData();
            int r = p.size() - 1;
            while (r >= 0 && data[r] == 0) {
                r--;
            }
            return Math.max(0, r);
        }

        public static void normalize(IntList list) {
            list.retain(rankOf(list) + 1);
        }

        public static void mul(IntList a, IntList b, IntList c, Modular mod) {
            int rA = rankOf(a);
            int rB = rankOf(b);
            c.clear();
            c.expandWith(0, rA + rB + 1);
            int[] aData = a.getData();
            int[] bData = b.getData();
            int[] cData = c.getData();
            for (int i = 0; i <= rA; i++) {
                for (int j = 0; j <= rB; j++) {
                    cData[i + j] = mod.plus(cData[i + j], mod.mul(aData[i], bData[j]));
                }
            }
        }

        public static void divide(IntList a, IntList b, IntList c, IntList remainder, Power pow) {
            Modular mod = pow.getModular();
            int rA = rankOf(a);
            int rB = rankOf(b);

            if (rA < rB) {
                c.clear();
                c.add(0);
                remainder.clear();
                remainder.addAll(a);
                return;
            }

            int rC = Math.max(0, rA - rB);
            c.clear();
            c.expandWith(0, rC + 1);
            remainder.clear();
            remainder.addAll(a);

            int[] bData = b.getData();
            int[] cData = c.getData();
            int[] rData = remainder.getData();

            if (extGCD.extgcd(b.get(rB), mod.getMod()) != 1) {
                throw new IllegalArgumentException();
            }
            int inv = mod.valueOf(extGCD.getX());
            for (int i = rA, j = rC; i >= rB; i--, j--) {
                if (rData[i] == 0) {
                    continue;
                }
                int factor = mod.mul(-rData[i], inv);
                cData[j] = mod.valueOf(-factor);
                for (int k = rB; k >= 0; k--) {
                    rData[k + j] = mod.plus(rData[k + j], mod.mul(factor, bData[k]));
                }
            }

            normalize(remainder);
        }

        public static void module(long k, IntList p, IntList remainder, Power pow) {
            int rP = rankOf(p);
            if (rP == 0) {
                remainder.clear();
                remainder.add(0);
                return;
            }

            IntList a = listBuffer.alloc();
            IntList c = listBuffer.alloc();

            module(k, a, p, c, remainder, rP, pow);

            listBuffer.release(a);
            listBuffer.release(c);
        }

        private static void module(long k, IntList a, IntList b, IntList c, IntList remainder, int rb, Power pow) {
            Modular mod = pow.getModular();
            if (k < rb) {
                remainder.clear();
                remainder.expandWith(0, (int) k + 1);
                remainder.set((int) k, 1);
                return;
            }
            module(k / 2, a, b, c, remainder, rb, pow);
            mul(remainder, remainder, a, mod);
            if (k % 2 == 1) {
                int ra = rankOf(a);
                a.expandWith(0, ra + 2);
                int[] aData = a.getData();
                for (int i = ra; i >= 0; i--) {
                    aData[i + 1] = aData[i];
                }
                aData[0] = 0;
            }
            divide(a, b, c, remainder, pow);
        }

    }

    static interface IntEntryIterator {
        boolean hasNext();

        void next();

        int getEntryKey();

        int getEntryValue();

    }

    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 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 Modular getModularForPowerComputation() {
            return new Modular(m - 1);
        }

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

    }

    static class PollardRho {
        MillerRabin mr = new MillerRabin();
        Gcd gcd = new Gcd();
        Random random = new Random();

        public int findFactor(int n) {
            if (mr.mr(n, 10)) {
                return n;
            }
            while (true) {
                int f = findFactor0(random.nextInt(n), random.nextInt(n), n);
                if (f != -1) {
                    return f;
                }
            }
        }

        public Map<Integer, Integer> findAllFactors(int n) {
            Map<Integer, Integer> map = new HashMap();
            findAllFactors(map, n);
            return map;
        }

        private void findAllFactors(Map<Integer, Integer> map, int n) {
            if (n == 1) {
                return;
            }
            int f = findFactor(n);
            if (f == n) {
                Integer value = map.get(f);
                if (value == null) {
                    value = 1;
                }
                map.put(f, value * f);
                return;
            }
            findAllFactors(map, f);
            findAllFactors(map, n / f);
        }

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

    }

    static class Power {
        final Modular modular;

        public Modular getModular() {
            return 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;
        }

    }
}