Problem: 2049C - MEX Cycle
Language: Java 8

Previous submission (verdict: Wrong answer on test 1):
import static java.lang.Math.max;

import static java.lang.Math.min;

import static java.lang.Math.abs;



import java.util.*;

import java.io.*;

import java.math.*;



public final class Main {



    static PrintWriter out = new PrintWriter(System.out);

    static FastReader in = new FastReader();

    static final int MOD1 = (int) (1e9 + 7);

    static final int MOD2 = 998244353;



    static final int inf = Integer.MAX_VALUE;

    static final int minf = Integer.MIN_VALUE;

    static final long linf = 1L << 62;



    public static void main(String[] args){

        int tt = i();

        while (tt-- > 0) {

            solve();

        }

        out.flush();

    }



    public static void solve(){



        // int MIN = -1*(int) 1e9;

        // int MAX = (int) 1e9;

        // PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder());



        int n = i();

        int x = i();

        int y = i();

        // String s = s();

        // int ar[]=input(n);

        int ar[]=new int[n];

        for(int i=0;i<n;i++){

            ar[i]=i&1;

        }

        if((n&1)==1){

            ar[0]=2;

        }

        if(abs(x-y)!=n-1&&abs(x-y)!=1&&!((n&1)==1&&(x==1||y==1))){

            ar[y-1]=2;

        }

        pl(ar);

    }



    static int BinarySearch(long ar[], int k) {

        int lo = 0;

        int hi = ar.length - 1;

        int mid;

        int ans = -1;

        while (lo <= hi) {

            mid = lo + ((hi - lo) / 2);

            if (ar[mid] >= k) {

                ans = mid;

                hi = mid - 1;

            } else {

                lo = mid + 1;

            }

        }

        return ans;

    }



    // ------------------------------------------COMMON|FUNCTIONS--------------------------------------------------//



    // -------------BINARYSEARCH-----------//



    // UPPERBOUND find lowest i which satisfy a[i]>=x

    static int upperbound(List<Integer> a, int x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a.get(m) >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    static int upperbound(List<Long> a, long x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a.get(m) >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    static int upperbound(int[] a, int x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a[m] >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    static int upperbound(long[] a, long x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a[m] >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    // LOWERBOUND find highest i which satisfy a[i]<=x

    static int lowerbound(List<Long> a, long x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a.get(m) <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    static int lowerbound(List<Integer> a, int x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a.get(m) <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    static int lowerbound(int[] a, int x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a[m] <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    static int lowerbound(long[] a, long x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a[m] <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    // -------------BINARYSEARCH-----------//



    // ---------------MATH-----------------//



    public static long fact(int n, int mod) {

        long res = 1;

        for (int i = 2; i <= n; i++) {

            res = (res * i) % mod;

        }

        return res;

    }



    static int GCD(int a, int b) {

        int dividend = a > b ? a : b;

        int divisor = a < b ? a : b;



        while (divisor > 0) {

            int reminder = dividend % divisor;

            dividend = divisor;

            divisor = reminder;

        }

        return dividend;

    }



    static long GCD(long a, long b) {

        long dividend = a > b ? a : b;

        long divisor = a < b ? a : b;



        while (divisor > 0) {

            long reminder = dividend % divisor;

            dividend = divisor;

            divisor = reminder;

        }

        return dividend;

    }



    static long LCM(int a, int b) {

        return (long) a / GCD(a, b) * b;

    }



    static long LCM(long a, long b) {

        return a / GCD(a, b) * b;

    }



    static long pow(long a, long b, int mod) {

        long pow = 1;

        long x = a;

        while (b != 0) {

            if ((b & 1) != 0) {

                pow = (pow * x) % mod;

            }

            x = (x * x) % mod;

            b /= 2;

        }

        return pow;

    }



    static long pow(long a, long b) {

        long pow = 1;

        long x = a;

        while (b != 0) {

            if ((b & 1) != 0) {

                pow *= x;

            }

            x = x * x;

            b /= 2;

        }

        return pow;

    }



    static long modInverse(long x, int mod) {

        return pow(x, mod - 2, mod);

    }



    static boolean isPrime(long N) {

        if (N <= 1) {

            return false;

        }

        if (N <= 3) {

            return true;

        }

        if (N % 2 == 0 || N % 3 == 0) {

            return false;

        }

        for (int i = 5; i * i <= N; i = i + 6) {

            if (N % i == 0 || N % (i + 2) == 0) {

                return false;

            }

        }

        return true;

    }



    static long log(long a) {

        return (long) (Math.log(a));

    }



    static long log2(long a) {

        return (long) (Math.log(a) / Math.log(2));

    }



    static long sqrt(long x) {

        long start = 0, end = (long) 3e9, ans = 1;

        while (start <= end) {

            long mid = (start + end) / 2;

            if (mid * mid <= x) {

                ans = mid;

                start = mid + 1;

            } else

                end = mid - 1;

        }

        return ans;

    }



    static long ceil(long a, long b) {

        return (a / b) + ((a % b == 0) ? 0 : 1);

    }



    static boolean isPerfectSquare(double number) {

        double sqrt = Math.sqrt(number);

        return ((sqrt - Math.floor(sqrt)) == 0);

    }



    // ---------------MATH-----------------//

    // ---------------CALCS-----------------//



    static long sum(List<Long> a) {

        long sum = 0;

        for (long ele : a)

            sum += ele;

        return sum;

    }



    static long sum(int[] a) {

        long sum = 0;

        for (int ele : a)

            sum += ele;

        return sum;

    }



    static long sum(long[] a) {

        long sum = 0;

        for (long ele : a)

            sum += ele;

        return sum;

    }



    static int maxArray(long a[]) {

        int in = 0;

        long m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] > m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    static int maxArray(int a[]) {

        int in = 0;

        int m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] > m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    static int minArray(long a[]) {

        int in = 0;

        long m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] < m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    static int minArray(int a[]) {

        int in = 0;

        int m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] < m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    // ---------------CALCS-----------------//



    // ------------------------------------------COMMON|FUNCTIONS--------------------------------------------------//



    // ------------------------------------------MODIFICATIONS--------------------------------------------------//



    static void shuffle(int[] arr) {

        for (int i = 0; i < arr.length; i++) {

            int rand = (int) (Math.random() * arr.length);

            int temp = arr[rand];

            arr[rand] = arr[i];

            arr[i] = temp;

        }

    }



    static void shuffleAndSort(int[] arr) {

        for (int i = 0; i < arr.length; i++) {

            int rand = (int) (Math.random() * arr.length);

            int temp = arr[rand];

            arr[rand] = arr[i];

            arr[i] = temp;

        }

        Arrays.sort(arr);

    }



    static void shuffleAndSort(long[] arr) {

        for (int i = 0; i < arr.length; i++) {

            int rand = (int) (Math.random() * arr.length);

            long temp = arr[rand];

            arr[rand] = arr[i];

            arr[i] = temp;

        }

        Arrays.sort(arr);

    }



    static void swap(int A[], int a, int b) {

        int t = A[a];

        A[a] = A[b];

        A[b] = t;

    }



    static void swap(long A[], int a, int b) {

        long t = A[a];

        A[a] = A[b];

        A[b] = t;

    }



    static void swap(char A[], int a, int b) {

        char t = A[a];

        A[a] = A[b];

        A[b] = t;

    }



    public static String reverse(String str) {

        if (str == null) {

            return null;

        }

        return new StringBuilder(str).reverse().toString();

    }



    public static void reverse(int[] arr) {

        int l = 0;

        int r = arr.length - 1;

        while (l < r) {

            swap(arr, l, r);

            l++;

            r--;

        }

    }



    public static void reverse(long[] arr) {

        int l = 0;

        int r = arr.length - 1;

        while (l < r) {

            swap(arr, l, r);

            l++;

            r--;

        }

    }



    public static String repeat(char ch, int repeat) {

        if (repeat <= 0) {

            return "";

        }

        final char[] buf = new char[repeat];

        for (int i = repeat - 1; i >= 0; i--) {

            buf[i] = ch;

        }

        return new String(buf);

    }



    public static String repeat(char ch[], int repeat) {

        if (repeat <= 0) {

            return "";

        }

        final char[] buf = new char[repeat];

        for (int i = 0; i < repeat; i++) {

            buf[i] = ch[i % ch.length];

        }

        return new String(buf);

    }



    public static String repeat(String ch, int repeat) {

        if (repeat <= 0) {

            return "";

        }

        final char[] buf = new char[repeat];

        for (int i = 0; i < repeat; i++) {

            buf[i] = ch.charAt(i % ch.length());

        }

        return new String(buf);

    }



    static void fillFrequency(Map<Long, Integer> map, long a[]) {

        for (int i = 0; i < a.length; i++) {

            fill(map, a[i]);

        }

    }



    static void fill(Map<Long, Integer> map, long val) {

        if (map.containsKey(val))

            map.put(val, map.get(val) + 1);

        else

            map.put(val, 1);

    }



    static void fillFrequency(Map<Integer, Integer> map, int a[]) {

        for (int i = 0; i < a.length; i++) {

            fill(map, a[i]);

        }

    }



    static void fill(Map<Integer, Integer> map, int val) {

        if (map.containsKey(val))

            map.put(val, map.get(val) + 1);

        else

            map.put(val, 1);

    }



    static void remove(Map<Long, Integer> map, long val) {

        if (map.get(val) == 1)

            map.remove(val);

        else

            map.replace(val, map.get(val) - 1);

    }



    static void remove(Map<Integer, Integer> map, int val) {

        if (map.get(val) == 1)

            map.remove(val);

        else

            map.replace(val, map.get(val) - 1);

    }



    // ------------------------------------------MODIFICATIONS--------------------------------------------------//    // -----------------------------------------------PRECOMPUTE--------------------------------------------------//



    // --------------BITS-----------------//

    static int[][] PrefixBitsCount(int n, int[] a) {

        int pref[][] = new int[n + 1][32];

        // Builds the prefix sums for each bit

        for (int i = 0; i < n; i++) {

            for (int j = 0; j < 32; j++) {

                if ((a[i] & (1 << j)) != 0) {

                    pref[i + 1][j] = pref[i][j] + 1;

                } else {

                    pref[i + 1][j] = pref[i][j];

                }

            }

        }

        return pref;

    }



    static int[] prefixAnd(int[] a) {

        int[] pre = new int[a.length];

        pre[0] = a[0];

        for (int i = 1; i < a.length; i++) {

            pre[i] = pre[i - 1] & a[i];

        }

        return pre;

    }



    static int[] prefixOr(int[] a) {

        int[] pre = new int[a.length];

        pre[0] = a[0];

        for (int i = 1; i < a.length; i++) {

            pre[i] = pre[i - 1] | a[i];

        }

        return pre;

    }



    static int[] prefixXor(int[] a) {

        int[] pre = new int[a.length];

        pre[0] = a[0];

        for (int i = 1; i < a.length; i++) {

            pre[i] = pre[i - 1] ^ a[i];

        }

        return pre;

    }

    // --------------BITS-----------------//



    // --------------ARRAYS-----------------//



    static int[] getPrefMax(int arr[]) {

        int n = arr.length;

        int pref[] = new int[n];

        pref[0] = arr[0];

        for (int i = 1; i < n; i++) {

            pref[i] = max(arr[i], pref[i - 1]);

        }

        return pref;

    }



    static int[] getPrefMin(int arr[]) {

        int n = arr.length;

        int pref[] = new int[n];

        pref[0] = arr[0];

        for (int i = 1; i < n; i++) {

            pref[i] = min(arr[i], pref[i - 1]);

        }

        return pref;

    }



    static int[] getSuffMin(int arr[]) {

        int n = arr.length;

        int suff[] = new int[n];

        suff[n - 1] = arr[n - 1];

        for (int i = n - 2; i >= 0; i--) {

            suff[i] = min(suff[i + 1], arr[i]);

        }

        return suff;

    }



    static long[] prefix(int[] a) {

        long[] pre = new long[a.length + 1];

        pre[0] = 0;

        for (int i = 0; i < a.length; i++) {

            pre[i + 1] = pre[i] + a[i];

        }

        return pre;

    }



    static List<Long> prefix(List<Integer> a) {

        List<Long> pre = new ArrayList<>();

        pre.add(0l);

        for (int i = 0; i < a.size(); i++) {

            pre.add(pre.get(i) + a.get(i));

        }

        return pre;

    }



    static long[] prefix(long[] a) {

        long[] pre = new long[a.length + 1];

        pre[0] = 0;

        for (int i = 0; i < a.length; i++) {

            pre[i + 1] = pre[i] + a[i];

        }

        return pre;

    }



    static long[] suffix(int[] a) {

        long[] post = new long[a.length + 1];

        post[a.length] = 0;

        for (int i = a.length - 1; i >= 0; i++) {

            post[i] = post[i + 1] + a[i];

        }

        return post;

    }



    static long[] suffix(long[] a) {

        long[] post = new long[a.length + 1];

        post[a.length] = 0;

        for (int i = a.length - 1; i >= 0; i++) {

            post[i] = post[i + 1] + a[i];

        }

        return post;

    }

    // --------------ARRAYS-----------------//



    // --------------Sieve&Factors-----------------//



    static List<Integer> sieveOfEratosthenes(int n) {

        List<Integer> primeList = new ArrayList<>();

        boolean prime[] = new boolean[n + 1];

        for (int i = 0; i <= n; i++)

            prime[i] = true;



        for (int p = 2; p * p <= n; p++) {



            if (prime[p] == true) {



                for (int i = p * p; i <= n; i += p)

                    prime[i] = false;

            }

        }



        for (int i = 2; i <= n; i++) {

            if (prime[i] == true)

                primeList.add(i);

            // System.out.print(i + " ");

        }

        return primeList;

    }



    static List<Integer> allDivisors(int n) {

        List<Integer> divisoers = new ArrayList<>();

        for (int i = 1; i * i <= n; i++) {

            if (n % i == 0) {

                divisoers.add(i);

                if (i != n / i) {

                    divisoers.add(n / i);

                }

            }

        }

        return divisoers;

    }



    // --------------Sieve&Factors-----------------//



    // -----------------------------------------------PRECOMPUTE--------------------------------------------------//



    // ---------------------------------------------INPUT&OUTPUT--------------------------------------------------//



    static int i() {

        return in.nextInt();

    }



    static long l() {

        return in.nextLong();

    }



    static double d() {

        return in.nextDouble();

    }



    static String s() {

        return in.nextLine();

    }



    static ArrayList<Integer> inputList(int n) {

        ArrayList<Integer> a = new ArrayList<Integer>(n);

        for (int i = 0; i < n; i++)

            a.add(i());

        return a;

    }



    static ArrayList<Long> inputListLong(int n) {

        ArrayList<Long> a = new ArrayList<Long>(n);

        for (int i = 0; i < n; i++)

            a.add(l());

        return a;

    }



    static int[][] inputWithIdx(int N) {

        int A[][] = new int[N][2];

        for (int i = 0; i < N; i++) {

            A[i] = new int[] { in.nextInt(), i };

        }

        return A;

    }



    static int[][] inputMatrix(int N, int M) {

        int A[][] = new int[N][M];

        for (int i = 0; i < N; i++) {

            for (int j = 0; j < M; j++) {

                A[i][j] = i();

            }

        }

        return A;

    }



    static long[][] inputMatrixLong(int N, int M) {

        long A[][] = new long[N][M];

        for (int i = 0; i < N; i++) {

            for (int j = 0; j < M; j++) {

                A[i][j] = i();

            }

        }

        return A;

    }



    static int[] input(int N) {

        int A[] = new int[N];

        for (int i = 0; i < N; i++) {

            A[i] = in.nextInt();

        }

        return A;

    }



    static Integer[] inputWrapper(int N) {

        Integer A[] = new Integer[N];

        for (int i = 0; i < N; i++) {

            A[i] = in.nextInt();

        }

        return A;

    }



    static long[] inputLong(int N) {

        long A[] = new long[N];

        for (int i = 0; i < A.length; i++) {

            A[i] = in.nextLong();

        }

        return A;

    }



    static void p(String s) {

        out.print(s);

    }



    static void p(int s) {

        out.print(s);

    }



    static void p(long s) {

        out.print(s);

    }



    static void p(double s) {

        out.print(s);

    }



    static void p(char s) {

        out.print(s);

    }



    static void pl(String s) {

        out.println(s);

    }



    static void pl(int s) {

        out.println(s);

    }



    static void pl(long s) {

        out.println(s);

    }



    static void pl(double s) {

        out.println(s);

    }



    static void pl(char c) {

        out.println(c);

    }



    static void pl() {

        out.println();

    }



    static void pl(int[] o) {

        for (int i = 0; i < o.length; i++) {

            out.print(o[i] + " ");

        }

        out.println();

    }



    static void pl(long[] o) {

        for (int i = 0; i < o.length; i++) {

            out.print(o[i] + " ");

        }

        out.println();

    }



    static <T> void pl(T[] o) {

        for (int i = 0; i < o.length; i++) {

            out.print(o[i] + " ");

        }

        out.println();

    }



    static <T> void pl(List<T> A) {

        for (T a : A) {

            out.print(a + " ");

        }

        out.println();

    }



    static void pl(Object o) {

        out.println(o);

    }



    static void ps(int s) {

        out.print(s + " ");

    }



    static void ps(long s) {

        out.print(s + " ");

    }



    static void ps(double s) {

        out.print(s + " ");

    }



    static void ps(char c) {

        out.print(c + " ");

    }



    static void yes() {

        pl("YES");

    }



    static void no() {

        pl("NO");

    }



    // ---------------------------------------------INPUT&OUTPUT--------------------------------------------------//



}



  class FastReader {



    BufferedReader br;

    StringTokenizer st;



    public FastReader() {

        br = new BufferedReader(new InputStreamReader(System.in));

    }



    String next() {

        while (st == null || !st.hasMoreElements()) {

            try {

                st = new StringTokenizer(br.readLine());

            } catch (IOException e) {

                e.printStackTrace();

            }

        }

        return st.nextToken();

    }



    char nextChar() {

        return next().charAt(0);

    }



    int nextInt() {

        return Integer.parseInt(next());

    }



    long nextLong() {

        return Long.parseLong(next());

    }



    double nextDouble() {

        return Double.parseDouble(next());

    }



    String nextLine() {

        String str = "";

        try {

            str = br.readLine();

        } catch (IOException e) {

            e.printStackTrace();

        }

        return str;

    }

}





Submission (verdict: Wrong answer on test 2):
import static java.lang.Math.max;

import static java.lang.Math.min;

import static java.lang.Math.abs;



import java.util.*;

import java.io.*;

import java.math.*;



public final class Main {



    static PrintWriter out = new PrintWriter(System.out);

    static FastReader in = new FastReader();

    static final int MOD1 = (int) (1e9 + 7);

    static final int MOD2 = 998244353;



    static final int inf = Integer.MAX_VALUE;

    static final int minf = Integer.MIN_VALUE;

    static final long linf = 1L << 62;



    public static void main(String[] args){

        int tt = i();

        while (tt-- > 0) {

            solve();

        }

        out.flush();

    }



    public static void solve(){



        // int MIN = -1*(int) 1e9;

        // int MAX = (int) 1e9;

        // PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder());



        int n = i();

        int x = i();

        int y = i();

        // String s = s();

        // int ar[]=input(n);

        int ar[]=new int[n];

        for(int i=0;i<n;i++){

            ar[i]=i&1;

        }

        if((n&1)==1){

            ar[0]=2;

        }

            if(ar[x-1]==ar[y-1])

            ar[y-1]=2;

        pl(ar);

    }



    static int BinarySearch(long ar[], int k) {

        int lo = 0;

        int hi = ar.length - 1;

        int mid;

        int ans = -1;

        while (lo <= hi) {

            mid = lo + ((hi - lo) / 2);

            if (ar[mid] >= k) {

                ans = mid;

                hi = mid - 1;

            } else {

                lo = mid + 1;

            }

        }

        return ans;

    }



    // ------------------------------------------COMMON|FUNCTIONS--------------------------------------------------//



    // -------------BINARYSEARCH-----------//



    // UPPERBOUND find lowest i which satisfy a[i]>=x

    static int upperbound(List<Integer> a, int x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a.get(m) >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    static int upperbound(List<Long> a, long x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a.get(m) >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    static int upperbound(int[] a, int x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a[m] >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    static int upperbound(long[] a, long x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = l + (r - l) / 2;

            if (a[m] >= x) {

                r = m;

            } else {

                l = m + 1;

            }



        }

        return r;

    }



    // LOWERBOUND find highest i which satisfy a[i]<=x

    static int lowerbound(List<Long> a, long x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a.get(m) <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    static int lowerbound(List<Integer> a, int x) {

        int l = 0;

        int r = a.size() - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a.get(m) <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    static int lowerbound(int[] a, int x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a[m] <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    static int lowerbound(long[] a, long x) {

        int l = 0;

        int r = a.length - 1;

        while (l < r) {

            int m = (l + r + 1) / 2;

            if (a[m] <= x) {

                l = m;

            } else {

                r = m - 1;

            }

        }

        return l;

    }



    // -------------BINARYSEARCH-----------//



    // ---------------MATH-----------------//



    public static long fact(int n, int mod) {

        long res = 1;

        for (int i = 2; i <= n; i++) {

            res = (res * i) % mod;

        }

        return res;

    }



    static int GCD(int a, int b) {

        int dividend = a > b ? a : b;

        int divisor = a < b ? a : b;



        while (divisor > 0) {

            int reminder = dividend % divisor;

            dividend = divisor;

            divisor = reminder;

        }

        return dividend;

    }



    static long GCD(long a, long b) {

        long dividend = a > b ? a : b;

        long divisor = a < b ? a : b;



        while (divisor > 0) {

            long reminder = dividend % divisor;

            dividend = divisor;

            divisor = reminder;

        }

        return dividend;

    }



    static long LCM(int a, int b) {

        return (long) a / GCD(a, b) * b;

    }



    static long LCM(long a, long b) {

        return a / GCD(a, b) * b;

    }



    static long pow(long a, long b, int mod) {

        long pow = 1;

        long x = a;

        while (b != 0) {

            if ((b & 1) != 0) {

                pow = (pow * x) % mod;

            }

            x = (x * x) % mod;

            b /= 2;

        }

        return pow;

    }



    static long pow(long a, long b) {

        long pow = 1;

        long x = a;

        while (b != 0) {

            if ((b & 1) != 0) {

                pow *= x;

            }

            x = x * x;

            b /= 2;

        }

        return pow;

    }



    static long modInverse(long x, int mod) {

        return pow(x, mod - 2, mod);

    }



    static boolean isPrime(long N) {

        if (N <= 1) {

            return false;

        }

        if (N <= 3) {

            return true;

        }

        if (N % 2 == 0 || N % 3 == 0) {

            return false;

        }

        for (int i = 5; i * i <= N; i = i + 6) {

            if (N % i == 0 || N % (i + 2) == 0) {

                return false;

            }

        }

        return true;

    }



    static long log(long a) {

        return (long) (Math.log(a));

    }



    static long log2(long a) {

        return (long) (Math.log(a) / Math.log(2));

    }



    static long sqrt(long x) {

        long start = 0, end = (long) 3e9, ans = 1;

        while (start <= end) {

            long mid = (start + end) / 2;

            if (mid * mid <= x) {

                ans = mid;

                start = mid + 1;

            } else

                end = mid - 1;

        }

        return ans;

    }



    static long ceil(long a, long b) {

        return (a / b) + ((a % b == 0) ? 0 : 1);

    }



    static boolean isPerfectSquare(double number) {

        double sqrt = Math.sqrt(number);

        return ((sqrt - Math.floor(sqrt)) == 0);

    }



    // ---------------MATH-----------------//

    // ---------------CALCS-----------------//



    static long sum(List<Long> a) {

        long sum = 0;

        for (long ele : a)

            sum += ele;

        return sum;

    }



    static long sum(int[] a) {

        long sum = 0;

        for (int ele : a)

            sum += ele;

        return sum;

    }



    static long sum(long[] a) {

        long sum = 0;

        for (long ele : a)

            sum += ele;

        return sum;

    }



    static int maxArray(long a[]) {

        int in = 0;

        long m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] > m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    static int maxArray(int a[]) {

        int in = 0;

        int m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] > m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    static int minArray(long a[]) {

        int in = 0;

        long m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] < m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    static int minArray(int a[]) {

        int in = 0;

        int m = a[0];

        for (int i = 1; i < a.length; i++) {

            if (a[i] < m) {

                m = a[i];

                in = i;

            }

        }

        return in;

    }



    // ---------------CALCS-----------------//



    // ------------------------------------------COMMON|FUNCTIONS--------------------------------------------------//



    // ------------------------------------------MODIFICATIONS--------------------------------------------------//



    static void shuffle(int[] arr) {

        for (int i = 0; i < arr.length; i++) {

            int rand = (int) (Math.random() * arr.length);

            int temp = arr[rand];

            arr[rand] = arr[i];

            arr[i] = temp;

        }

    }



    static void shuffleAndSort(int[] arr) {

        for (int i = 0; i < arr.length; i++) {

            int rand = (int) (Math.random() * arr.length);

            int temp = arr[rand];

            arr[rand] = arr[i];

            arr[i] = temp;

        }

        Arrays.sort(arr);

    }



    static void shuffleAndSort(long[] arr) {

        for (int i = 0; i < arr.length; i++) {

            int rand = (int) (Math.random() * arr.length);

            long temp = arr[rand];

            arr[rand] = arr[i];

            arr[i] = temp;

        }

        Arrays.sort(arr);

    }



    static void swap(int A[], int a, int b) {

        int t = A[a];

        A[a] = A[b];

        A[b] = t;

    }



    static void swap(long A[], int a, int b) {

        long t = A[a];

        A[a] = A[b];

        A[b] = t;

    }



    static void swap(char A[], int a, int b) {

        char t = A[a];

        A[a] = A[b];

        A[b] = t;

    }



    public static String reverse(String str) {

        if (str == null) {

            return null;

        }

        return new StringBuilder(str).reverse().toString();

    }



    public static void reverse(int[] arr) {

        int l = 0;

        int r = arr.length - 1;

        while (l < r) {

            swap(arr, l, r);

            l++;

            r--;

        }

    }



    public static void reverse(long[] arr) {

        int l = 0;

        int r = arr.length - 1;

        while (l < r) {

            swap(arr, l, r);

            l++;

            r--;

        }

    }



    public static String repeat(char ch, int repeat) {

        if (repeat <= 0) {

            return "";

        }

        final char[] buf = new char[repeat];

        for (int i = repeat - 1; i >= 0; i--) {

            buf[i] = ch;

        }

        return new String(buf);

    }



    public static String repeat(char ch[], int repeat) {

        if (repeat <= 0) {

            return "";

        }

        final char[] buf = new char[repeat];

        for (int i = 0; i < repeat; i++) {

            buf[i] = ch[i % ch.length];

        }

        return new String(buf);

    }



    public static String repeat(String ch, int repeat) {

        if (repeat <= 0) {

            return "";

        }

        final char[] buf = new char[repeat];

        for (int i = 0; i < repeat; i++) {

            buf[i] = ch.charAt(i % ch.length());

        }

        return new String(buf);

    }



    static void fillFrequency(Map<Long, Integer> map, long a[]) {

        for (int i = 0; i < a.length; i++) {

            fill(map, a[i]);

        }

    }



    static void fill(Map<Long, Integer> map, long val) {

        if (map.containsKey(val))

            map.put(val, map.get(val) + 1);

        else

            map.put(val, 1);

    }



    static void fillFrequency(Map<Integer, Integer> map, int a[]) {

        for (int i = 0; i < a.length; i++) {

            fill(map, a[i]);

        }

    }



    static void fill(Map<Integer, Integer> map, int val) {

        if (map.containsKey(val))

            map.put(val, map.get(val) + 1);

        else

            map.put(val, 1);

    }



    static void remove(Map<Long, Integer> map, long val) {

        if (map.get(val) == 1)

            map.remove(val);

        else

            map.replace(val, map.get(val) - 1);

    }



    static void remove(Map<Integer, Integer> map, int val) {

        if (map.get(val) == 1)

            map.remove(val);

        else

            map.replace(val, map.get(val) - 1);

    }



    // ------------------------------------------MODIFICATIONS--------------------------------------------------//    // -----------------------------------------------PRECOMPUTE--------------------------------------------------//



    // --------------BITS-----------------//

    static int[][] PrefixBitsCount(int n, int[] a) {

        int pref[][] = new int[n + 1][32];

        // Builds the prefix sums for each bit

        for (int i = 0; i < n; i++) {

            for (int j = 0; j < 32; j++) {

                if ((a[i] & (1 << j)) != 0) {

                    pref[i + 1][j] = pref[i][j] + 1;

                } else {

                    pref[i + 1][j] = pref[i][j];

                }

            }

        }

        return pref;

    }



    static int[] prefixAnd(int[] a) {

        int[] pre = new int[a.length];

        pre[0] = a[0];

        for (int i = 1; i < a.length; i++) {

            pre[i] = pre[i - 1] & a[i];

        }

        return pre;

    }



    static int[] prefixOr(int[] a) {

        int[] pre = new int[a.length];

        pre[0] = a[0];

        for (int i = 1; i < a.length; i++) {

            pre[i] = pre[i - 1] | a[i];

        }

        return pre;

    }



    static int[] prefixXor(int[] a) {

        int[] pre = new int[a.length];

        pre[0] = a[0];

        for (int i = 1; i < a.length; i++) {

            pre[i] = pre[i - 1] ^ a[i];

        }

        return pre;

    }

    // --------------BITS-----------------//



    // --------------ARRAYS-----------------//



    static int[] getPrefMax(int arr[]) {

        int n = arr.length;

        int pref[] = new int[n];

        pref[0] = arr[0];

        for (int i = 1; i < n; i++) {

            pref[i] = max(arr[i], pref[i - 1]);

        }

        return pref;

    }



    static int[] getPrefMin(int arr[]) {

        int n = arr.length;

        int pref[] = new int[n];

        pref[0] = arr[0];

        for (int i = 1; i < n; i++) {

            pref[i] = min(arr[i], pref[i - 1]);

        }

        return pref;

    }



    static int[] getSuffMin(int arr[]) {

        int n = arr.length;

        int suff[] = new int[n];

        suff[n - 1] = arr[n - 1];

        for (int i = n - 2; i >= 0; i--) {

            suff[i] = min(suff[i + 1], arr[i]);

        }

        return suff;

    }



    static long[] prefix(int[] a) {

        long[] pre = new long[a.length + 1];

        pre[0] = 0;

        for (int i = 0; i < a.length; i++) {

            pre[i + 1] = pre[i] + a[i];

        }

        return pre;

    }



    static List<Long> prefix(List<Integer> a) {

        List<Long> pre = new ArrayList<>();

        pre.add(0l);

        for (int i = 0; i < a.size(); i++) {

            pre.add(pre.get(i) + a.get(i));

        }

        return pre;

    }



    static long[] prefix(long[] a) {

        long[] pre = new long[a.length + 1];

        pre[0] = 0;

        for (int i = 0; i < a.length; i++) {

            pre[i + 1] = pre[i] + a[i];

        }

        return pre;

    }



    static long[] suffix(int[] a) {

        long[] post = new long[a.length + 1];

        post[a.length] = 0;

        for (int i = a.length - 1; i >= 0; i++) {

            post[i] = post[i + 1] + a[i];

        }

        return post;

    }



    static long[] suffix(long[] a) {

        long[] post = new long[a.length + 1];

        post[a.length] = 0;

        for (int i = a.length - 1; i >= 0; i++) {

            post[i] = post[i + 1] + a[i];

        }

        return post;

    }

    // --------------ARRAYS-----------------//



    // --------------Sieve&Factors-----------------//



    static List<Integer> sieveOfEratosthenes(int n) {

        List<Integer> primeList = new ArrayList<>();

        boolean prime[] = new boolean[n + 1];

        for (int i = 0; i <= n; i++)

            prime[i] = true;



        for (int p = 2; p * p <= n; p++) {



            if (prime[p] == true) {



                for (int i = p * p; i <= n; i += p)

                    prime[i] = false;

            }

        }



        for (int i = 2; i <= n; i++) {

            if (prime[i] == true)

                primeList.add(i);

            // System.out.print(i + " ");

        }

        return primeList;

    }



    static List<Integer> allDivisors(int n) {

        List<Integer> divisoers = new ArrayList<>();

        for (int i = 1; i * i <= n; i++) {

            if (n % i == 0) {

                divisoers.add(i);

                if (i != n / i) {

                    divisoers.add(n / i);

                }

            }

        }

        return divisoers;

    }



    // --------------Sieve&Factors-----------------//



    // -----------------------------------------------PRECOMPUTE--------------------------------------------------//



    // ---------------------------------------------INPUT&OUTPUT--------------------------------------------------//



    static int i() {

        return in.nextInt();

    }



    static long l() {

        return in.nextLong();

    }



    static double d() {

        return in.nextDouble();

    }



    static String s() {

        return in.nextLine();

    }



    static ArrayList<Integer> inputList(int n) {

        ArrayList<Integer> a = new ArrayList<Integer>(n);

        for (int i = 0; i < n; i++)

            a.add(i());

        return a;

    }



    static ArrayList<Long> inputListLong(int n) {

        ArrayList<Long> a = new ArrayList<Long>(n);

        for (int i = 0; i < n; i++)

            a.add(l());

        return a;

    }



    static int[][] inputWithIdx(int N) {

        int A[][] = new int[N][2];

        for (int i = 0; i < N; i++) {

            A[i] = new int[] { in.nextInt(), i };

        }

        return A;

    }



    static int[][] inputMatrix(int N, int M) {

        int A[][] = new int[N][M];

        for (int i = 0; i < N; i++) {

            for (int j = 0; j < M; j++) {

                A[i][j] = i();

            }

        }

        return A;

    }



    static long[][] inputMatrixLong(int N, int M) {

        long A[][] = new long[N][M];

        for (int i = 0; i < N; i++) {

            for (int j = 0; j < M; j++) {

                A[i][j] = i();

            }

        }

        return A;

    }



    static int[] input(int N) {

        int A[] = new int[N];

        for (int i = 0; i < N; i++) {

            A[i] = in.nextInt();

        }

        return A;

    }



    static Integer[] inputWrapper(int N) {

        Integer A[] = new Integer[N];

        for (int i = 0; i < N; i++) {

            A[i] = in.nextInt();

        }

        return A;

    }



    static long[] inputLong(int N) {

        long A[] = new long[N];

        for (int i = 0; i < A.length; i++) {

            A[i] = in.nextLong();

        }

        return A;

    }



    static void p(String s) {

        out.print(s);

    }



    static void p(int s) {

        out.print(s);

    }



    static void p(long s) {

        out.print(s);

    }



    static void p(double s) {

        out.print(s);

    }



    static void p(char s) {

        out.print(s);

    }



    static void pl(String s) {

        out.println(s);

    }



    static void pl(int s) {

        out.println(s);

    }



    static void pl(long s) {

        out.println(s);

    }



    static void pl(double s) {

        out.println(s);

    }



    static void pl(char c) {

        out.println(c);

    }



    static void pl() {

        out.println();

    }



    static void pl(int[] o) {

        for (int i = 0; i < o.length; i++) {

            out.print(o[i] + " ");

        }

        out.println();

    }



    static void pl(long[] o) {

        for (int i = 0; i < o.length; i++) {

            out.print(o[i] + " ");

        }

        out.println();

    }



    static <T> void pl(T[] o) {

        for (int i = 0; i < o.length; i++) {

            out.print(o[i] + " ");

        }

        out.println();

    }



    static <T> void pl(List<T> A) {

        for (T a : A) {

            out.print(a + " ");

        }

        out.println();

    }



    static void pl(Object o) {

        out.println(o);

    }



    static void ps(int s) {

        out.print(s + " ");

    }



    static void ps(long s) {

        out.print(s + " ");

    }



    static void ps(double s) {

        out.print(s + " ");

    }



    static void ps(char c) {

        out.print(c + " ");

    }



    static void yes() {

        pl("YES");

    }



    static void no() {

        pl("NO");

    }



    // ---------------------------------------------INPUT&OUTPUT--------------------------------------------------//



}



  class FastReader {



    BufferedReader br;

    StringTokenizer st;



    public FastReader() {

        br = new BufferedReader(new InputStreamReader(System.in));

    }



    String next() {

        while (st == null || !st.hasMoreElements()) {

            try {

                st = new StringTokenizer(br.readLine());

            } catch (IOException e) {

                e.printStackTrace();

            }

        }

        return st.nextToken();

    }



    char nextChar() {

        return next().charAt(0);

    }



    int nextInt() {

        return Integer.parseInt(next());

    }



    long nextLong() {

        return Long.parseLong(next());

    }



    double nextDouble() {

        return Double.parseDouble(next());

    }



    String nextLine() {

        String str = "";

        try {

            str = br.readLine();

        } catch (IOException e) {

            e.printStackTrace();

        }

        return str;

    }

}