You are given a string s consisting of lowercase English letters and a number k. Let's call a string consisting of lowercase English letters beautiful if the number of occurrences of each letter in that string is divisible by k. You are asked to find the lexicographically smallest beautiful string of length n, which is lexicographically greater or equal to string s. If such a string does not exist, output -1.

A string a is lexicographically smaller than a string b if and only if one of the following holds: 

  * a is a prefix of b, but a ≠ b; 
  * in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b. 

Input

The first line contains a single integer T (1 ≤ T ≤ 10 000) — the number of test cases.

The next 2 ⋅ T lines contain the description of test cases. The description of each test case consists of two lines.

The first line of the description contains two integers n and k (1 ≤ k ≤ n ≤ 10^5) — the length of string s and number k respectively.

The second line contains string s consisting of lowercase English letters.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case output in a separate line lexicographically smallest beautiful string of length n, which is greater or equal to string s, or -1 if such a string does not exist.

Example

Input


4
4 2
abcd
3 1
abc
4 3
aaaa
9 3
abaabaaaa


Output


acac
abc
-1
abaabaaab

Note

In the first test case "acac" is greater than or equal to s, and each letter appears 2 or 0 times in it, so it is beautiful.

In the second test case each letter appears 0 or 1 times in s, so s itself is the answer.

We can show that there is no suitable string in the third test case.

In the fourth test case each letter appears 0, 3, or 6 times in "abaabaaab". All these integers are divisible by 3.
import java.io.*;
import java.util.*;
import java.util.ArrayList;
import java.util.Arrays.*;
import static java.util.Collections.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf {
    static final int SCAN_LINE_LENGTH = 1_000_002;
    private static final boolean thread = false;
    @SuppressWarnings("all")
    static final boolean HAS_TEST_CASES = (1 == 1) ? true : false;

    static int n, a[], e[][], vis[], m, b[];
    @SuppressWarnings("all")
    private static Vector<Integer> adj[], v = new Vector<>();

    @SuppressWarnings("unchecked")
    static void solve() throws Exception {
        int n = ni(), k = ni();
        char[] s = n().toCharArray();
        if (n % k != 0) {
            pn(-1);
            return;
        }
        int[] f = new int[26];
        for (int i = 0; i < s.length; i++) {
            f[s[i] - 'a']++;
        }
        boolean b = true;
        for (int i : f) {
            if (i % k != 0)
                b = false;
        }
        if (b) {
            pn(new String(s));
            return;
        }
        for (int i = n - 1; i >= 0; i--) {
            char ch = s[i];
            f[ch - 'a']--;
            for (char j = (char) (s[i] + 1); j <= 'z'; j++) {
                s[i] = j;
                f[s[i] - 'a']++;
                if (check(s, k, f, i)) {
                    pn(new String(s));
                    return;
                }
                f[s[i] - 'a']--;
            }
            s[i] = ch;
        }
        pn(-1);
    }

    private static boolean check(char[] s, int k, int[] f, int i) {
        int c = 0;
        for (int j : f) {
            if (j > 0 && j % k != 0)
                c += (k - (j % k));
        }
        if (i + 1 + c > s.length)
            return false;
        ArrayList<Character> to = new ArrayList<>();
        for (int j = 0; j < f.length; j++) {
            if (f[j] % k > 0) {
                int t = (k - (f[j] % k));
                while (t-- > 0) {
                    to.add((char) ('a' + j));
                }
            }
        }
        while (to.size() + i + 1 < s.length) {
            to.add('a');
        }
        sort(to);
        i++;
        int j = 0;
        while (i < s.length) {
            s[i++] = to.get(j++);
        }
        return true;
    }

    public static void main(final String[] args) throws Exception {
        if (!thread) {
            final int testcases = HAS_TEST_CASES ? ni() : 1;
            for (int i = 1; i <= testcases; i++) {
                // pni(i + " t");
                // out.print("Case #" + (i + 1) + ": ");
                try {
                    solve();
                } catch (final Exception e) {
                    // pni("idk Exception");
                    // e.printStackTrace(System.err);
                    // System.exit(0);
                    pni(i);
                    throw e;
                }
            }
            out.flush();
        }
        r.close();
        out.close();
    }

    @SuppressWarnings("all")
    private static final int MOD = (int) (1e9 + 7), MOD_FFT = 998244353;
    private static final Reader r = new Reader();
    private static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    public static long[] enumPows(int a, int n, int mod) {
        a %= mod;
        long[] pows = new long[n + 1];
        pows[0] = 1;
        for (int i = 1; i <= n; i++)
            pows[i] = pows[i - 1] * a % mod;
        return pows;
    }

    @SuppressWarnings("all")
    private static boolean eq(long a, long b) {
        return Long.compare(a, b) == 0;
    }

    @SuppressWarnings("all")
    private static ArrayList<Integer> seive(int n) {
        ArrayList<Integer> p = new ArrayList<>();
        int[] f = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            if (f[i] == 1)
                continue;
            for (int j = i * i; j <= n && j < f.length; j += i) {
                f[j] = 1;
            }
        }
        for (int i = 2; i < f.length; i++) {
            if (f[i] == 0)
                p.add(i);
        }
        return p;
    }

    @SuppressWarnings("all")
    private static void s(int[] a) {
        Integer[] t = new Integer[a.length];
        for (int i = 0; i < t.length; i++) {
            t[i] = a[i];
        }
        sort(t);
        for (int i = 0; i < t.length; i++) {
            a[i] = t[i];
        }
    }

    int pow(int a, int b, int m) {
        int ans = 1;
        while (b != 0) {
            if ((b & 1) != 0)
                ans = (ans * a) % m;
            b /= 2;
            a = (a * a) % m;
        }
        return ans;
    }

    int modinv(int k) {
        return pow(k, MOD - 2, MOD);
    }

    @SuppressWarnings("all")
    private static void swap(final int i, final int j) {
        final int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    @SuppressWarnings("all")
    private static boolean isMulOverflow(final long A, final long B) {
        if (A == 0 || B == 0)
            return false;
        final long result = A * B;
        if (A == result / B)
            return true;
        return false;
    }

    @SuppressWarnings("all")
    private static int gcd(final int a, final int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    @SuppressWarnings("all")
    private static long gcd(final long a, final long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    @SuppressWarnings("all")
    private static class Pair<T, E> implements Comparable<Pair<T, E>> {
        T fir;
        E snd;

        Pair() {
        }

        Pair(final T x, final E y) {
            this.fir = x;
            this.snd = y;
        }

        // @Override
        // @SuppressWarnings("unchecked")
        // public int compareTo(final Pair<T, E> o) {
        // final int c = ((Comparable<T>) fir).compareTo(o.fir);
        // return c != 0 ? c : ((Comparable<E>) snd).compareTo(o.snd);
        // }
        @Override
        @SuppressWarnings("unchecked")
        public int compareTo(final Pair<T, E> o) {
            final int c = ((Comparable<T>) fir).compareTo(o.fir);
            return c;
        }

    }

    @SuppressWarnings("all")
    private static class pi implements Comparable<pi> {
        int fir, snd;

        pi() {
        }

        pi(final int a, final int b) {
            fir = a;
            snd = b;
        }

        public int compareTo(final pi o) {
            return fir == o.fir ? snd - o.snd : fir - o.fir;
        }

        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + fir;
            result = prime * result + snd;
            return result;
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            pi other = (pi) obj;
            if (fir != other.fir)
                return false;
            if (snd != other.snd)
                return false;
            return true;
        }

    }

    @SuppressWarnings("all")
    private static <T> void checkV(final Vector<T> adj[], final int i) {
        adj[i] = adj[i] == null ? new Vector<>() : adj[i];
    }

    @SuppressWarnings("all")
    private static int[] na(final int n) throws Exception {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }

    @SuppressWarnings("all")
    private static int[] na1(final int n) throws Exception {
        final int[] a = new int[n + 1];
        for (int i = 1; i < a.length; i++) {
            a[i] = ni();
        }
        return a;
    }

    @SuppressWarnings("all")
    private static String n() throws IOException {
        return r.readToken();
    }

    @SuppressWarnings("all")
    private static char[] ns() throws IOException {
        return r.readToken().toCharArray();
    }

    @SuppressWarnings("all")
    private static String nln() throws IOException {
        return r.readLine();
    }

    private static int ni() throws IOException {
        return r.nextInt();
    }

    @SuppressWarnings("all")
    private static long nl() throws IOException {
        return r.nextLong();
    }

    @SuppressWarnings("all")
    private static double nd() throws IOException {
        return r.nextDouble();
    }

    @SuppressWarnings("all")
    private static void p(final Object o) {
        out.print(o);
    }

    @SuppressWarnings("all")
    private static void pn(final Object o) {
        out.println(o);
    }

    @SuppressWarnings("all")
    private static void pn() {
        out.println("");
    }

    @SuppressWarnings("all")
    private static void pi(final Object o) {
        out.print(o);
        out.flush();
    }

    @SuppressWarnings("all")
    private static void pni() {
        out.println("");
        out.flush();
    }

    private static void pni(final Object o) {
        out.println(o);
        out.flush();
    }

    private static class Reader {
        private final int BUFFER_SIZE = 1 << 17;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        // private StringTokenizer st;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        @SuppressWarnings("all")
        public Reader(final String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        final byte[] buf = new byte[SCAN_LINE_LENGTH];

        public String readLine() throws IOException {
            int cnt = 0;
            int c;
            o: while ((c = read()) != -1) {
                if (c == '\n')
                    if (cnt == 0)
                        continue o;
                    else
                        break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String readToken() throws IOException {
            int cnt = 0;
            int c;
            o: while ((c = read()) != -1) {
                if (!(c >= 33 && c <= 126))
                    if (cnt == 0)
                        continue o;
                    else
                        break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    // static {
    // if (thread)
    // new Thread(null, new Runnable() {
    // @Override
    // public void run() {
    // try {
    // final int testcases = HAS_TEST_CASES ? ni() : 1;
    // for (int i = 1; i <= testcases; i++) {
    // // out.print("Case #" + (i + 1) + ": ");
    // try {
    // solve();
    // } catch (final ArrayIndexOutOfBoundsException e) {
    // e.printStackTrace(System.err);
    // System.exit(-1);
    // } catch (final Exception e) {
    // pni("idk Exception in solve");
    // e.printStackTrace(System.err);
    // System.exit(-1);
    // }
    // }
    // out.flush();
    // } catch (final Throwable t) {
    // t.printStackTrace(System.err);
    // System.exit(-1);
    // }
    // }
    // }, "rec", (1L << 28)).start();
    // }

    @SuppressWarnings({ "all", })
    private static <T> T deepCopy(final T old) {
        try {
            return (T) deepCopyObject(old);
        } catch (final IOException | ClassNotFoundException e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
        return null;
    }

    private static Object deepCopyObject(final Object oldObj) throws IOException, ClassNotFoundException {
        ObjectOutputStream oos = null;
        ObjectInputStream ois = null;
        try {
            final ByteArrayOutputStream bos = new ByteArrayOutputStream(); // A
            oos = new ObjectOutputStream(bos); // B
            // serialize and pass the object
            oos.writeObject(oldObj); // C
            oos.flush(); // D
            final ByteArrayInputStream bin = new ByteArrayInputStream(bos.toByteArray()); // E
            ois = new ObjectInputStream(bin); // F
            // return the new object
            return ois.readObject(); // G
        } catch (final ClassNotFoundException e) {
            pni("Exception in ObjectCloner = " + e);
            throw (e);
        } finally {
            oos.close();
            ois.close();
        }
    }

}