Problem: Merge sort is a well-known sorting algorithm. The main function that sorts the elements of array a with indices from [l, r) can be implemented as follows:

  1. If the segment [l, r) is already sorted in non-descending order (that is, for any i such that l ≤ i < r - 1 a[i] ≤ a[i + 1]), then end the function call; 
  2. Let <image>; 
  3. Call mergesort(a, l, mid); 
  4. Call mergesort(a, mid, r); 
  5. Merge segments [l, mid) and [mid, r), making the segment [l, r) sorted in non-descending order. The merge algorithm doesn't call any other functions. 



The array in this problem is 0-indexed, so to sort the whole array, you need to call mergesort(a, 0, n).

The number of calls of function mergesort is very important, so Ivan has decided to calculate it while sorting the array. For example, if a = {1, 2, 3, 4}, then there will be 1 call of mergesort — mergesort(0, 4), which will check that the array is sorted and then end. If a = {2, 1, 3}, then the number of calls is 3: first of all, you call mergesort(0, 3), which then sets mid = 1 and calls mergesort(0, 1) and mergesort(1, 3), which do not perform any recursive calls because segments (0, 1) and (1, 3) are sorted.

Ivan has implemented the program that counts the number of mergesort calls, but now he needs to test it. To do this, he needs to find an array a such that a is a permutation of size n (that is, the number of elements in a is n, and every integer number from [1, n] can be found in this array), and the number of mergesort calls when sorting the array is exactly k.

Help Ivan to find an array he wants!

Input

The first line contains two numbers n and k (1 ≤ n ≤ 100000, 1 ≤ k ≤ 200000) — the size of a desired permutation and the number of mergesort calls required to sort it.

Output

If a permutation of size n such that there will be exactly k calls of mergesort while sorting it doesn't exist, output  - 1. Otherwise output n integer numbers a[0], a[1], ..., a[n - 1] — the elements of a permutation that would meet the required conditions. If there are multiple answers, print any of them.

Examples

Input

3 3


Output

2 1 3 

Input

4 1


Output

1 2 3 4 

Input

5 6


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Solution {


    static MyScanner sc;
    private static PrintWriter out;
    static long M = 1000000007;


    public static void main(String[] s) throws Exception {
        StringBuilder stringBuilder = new StringBuilder();


//        stringBuilder.append("4 2 2" +
//                "  0 1" +
//                "  0 0 " +
//                "  0 1" +
//                "  0 1 ");
//        Random r = new Random(5);
//        for (int i = 0; i < 100000; i++) {
//            for (int j = 0; j < 4; j++) {
//                stringBuilder.append((char) (r.nextInt(2) + 'a'));
//            }
//            stringBuilder.append(' ');
//        }
//        for (int i = 0; i < 100000; i++) {
//            stringBuilder.append("1 ");
//            stringBuilder.append(r.nextInt(10) + 2);
//            stringBuilder.append(' ');
//            stringBuilder.append(r.nextInt(10) + 12);
//            stringBuilder.append(' ');
//        }

//
//        stringBuilder.append("10 20\real" +
//                "qn jq wkcexecmdkm bak xrkjwqdyu ossvo oat mbyx xnagxbwe gzay\real" +
//                "2 7 onzpq\real" +
//                "1 4 10\real" +
//                "2 9 xnagta\real" +
//                "2 7 o\real" +
//                "2 7 y\real" +
//                "1 5 6\real" +
//                "1 1 2\real" +
//                "2 2 jhulkujid\real" +
//                "1 3 10\real" +
//                "2 7 cl\real" +
//                "1 3 6\real" +
//                "1 5 10\real" +
//                "1 1 5\real" +
//                "2 3 wkc\real" +
//                "1 3 6\real" +
//                "2 1 qnwvjal\real" +
//                "2 1 qnwvncksizgza\real" +
//                "2 4 bh\real" +
//                "1 3 6\real" +
//                "1 7 10");
//

        if (stringBuilder.length() == 0) {
            sc = new MyScanner(System.in);
        } else {
            sc = new MyScanner(new BufferedReader(new StringReader(stringBuilder.toString())));
        }

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

        initData();
        solve();
        out.flush();
    }


    private static void initData() {
    }


    private static void solve() throws IOException {
        int n = sc.nextInt();
        int k = sc.nextInt();

        long[] max = new long[n + 1];
        max[0] = 1;
        max[1] = 1;
        for (int l = 2; l <= n; l++) {
            max[l] = max[l / 2] + max[(l + 1) / 2] + 1;
        }
        if (k > max[n] || k % 2 == 0) {
            out.println(-1);
            return;
        }
        printP(0, n, k, max);
    }

    private static void printP(int i, int n, long k, long[] max) {
        if (k == 1) {
            for (int l = i; l < n; l++) {
                out.print(l + 1 + " ");
            }
            return;
        }
        k--;
        int l = n - i;
        int bt = l / 2;


        int mid = n - bt;


        long kk1 = max[(n - i) / 2];
        if (kk1 >= k) {
            kk1 = k - 1;
        }
        long kk2 = k - kk1;


        printP(mid, n, kk1, max);
        printP(i, mid, kk2, max);

    }

    private static void solve3() throws IOException {
        int n = sc.nextInt();
        int m = sc.nextInt();


        STree s1 = new STree(n, true);

        int[] mmm = new int[n - 1];


        String[] k = new String[n];
        for (int i = 0; i < n; i++) {
            k[i] = sc.next();
            s1.put(i, k[i].length());
            if (i > 0) {
                mmm[i - 1] = lcp(k[i], k[i - 1]);
            }
        }
        SegmentTreeSegPos segmentTreeSegPos = new SegmentTreeSegPos(mmm);

        for (int r = 0; r < m; r++) {
            int t = sc.nextInt();
            if (t == 1) {
                int ll = sc.nextInt() - 1;
                int rr = sc.nextInt() - 1;
                long v1 = s1.max(ll, rr);
                if (rr > ll) {
                    v1 = Math.max(segmentTreeSegPos.max(ll, rr), v1);
                }
                out.println(v1);
            } else {
                int p = sc.nextInt() - 1;
                String ttt = sc.next();
                k[p] = ttt;
                s1.put(p, ttt.length());
                if (p > 0) {
                    mmm[p - 1] = lcp(k[p], k[p - 1]);
                    segmentTreeSegPos.update(p - 1, mmm[p - 1]);
                }
                if (p < n - 1) {
                    mmm[p] = lcp(k[p], k[p + 1]);
                    segmentTreeSegPos.update(p, mmm[p]);
                }
            }
        }

    }


    public static class SegmentTreeSegPos {
        public int total, half, real;
        public int[][] vasc;
        public int[][] pasc;
        public int[][] vdesc;
        public int[][] pdesc;
        public long[] maxs;
        public int[] lens;

        // one word
        public SegmentTreeSegPos(int[] a) {
            real = a.length;
            total = Integer.highestOneBit(Math.max(real - 1, 1)) << 2;
            half = total >>> 1;
            vasc = new int[total][];
            pasc = new int[total][];
            vdesc = new int[total][];
            pdesc = new int[total][];
            maxs = new long[total];
            lens = new int[total];
            for (int i = 0; i < real; i++) {
                vasc[half + i] = new int[]{a[i]};
                pasc[half + i] = new int[]{0}; // first appeared
                vdesc[half + i] = new int[]{a[i]};
                pdesc[half + i] = new int[]{0}; // last appeared
                maxs[half + i] = a[i] * 2;
                lens[half + i] = 1;
            }
            for (int i = real; i < half; i++) {
                vasc[half + i] = new int[0];
                pasc[half + i] = new int[0];
                vdesc[half + i] = new int[0];
                pdesc[half + i] = new int[0];
                lens[half + i] = 0;
            }
            for (int i = half - 1; i >= 1; i--) {
                propagate(i);
            }
        }

        int[][] merge(int[] v1, int[] p1, int[] v2, int[] p2) {
            int[] rv = Arrays.copyOf(v2, v2.length + v1.length);
            int[] rp = Arrays.copyOf(p2, v2.length + v1.length);
            int p = v2.length;
            int last = p > 0 ? p2[p - 1] : -1;
            for (int i = 0; i < v1.length; i++) {
                if (p > 0 && rv[p - 1] <= v1[i]) {
                    rp[p - 1] = p2[p - 1] + p1[i] + 1;
                } else if (p == 0 || rv[p - 1] > v1[i]) {
                    rv[p] = v1[i];
                    rp[p++] = last + p1[i] + 1;
                }
            }
            return new int[][]{
                    Arrays.copyOf(rv, p),
                    Arrays.copyOf(rp, p)
            };
        }

        private void tr(Object... o) {
            System.out.println(Arrays.deepToString(o));
        }

        private void propagate(int i) {
            int[][] res = merge(vasc[2 * i], pasc[2 * i], vasc[2 * i + 1], pasc[2 * i + 1]);
            vasc[i] = res[0];
            pasc[i] = res[1];

            res = merge(vdesc[2 * i + 1], pdesc[2 * i + 1], vdesc[2 * i], pdesc[2 * i]);
            vdesc[i] = res[0];
            pdesc[i] = res[1];

            lens[i] = lens[2 * i] + lens[2 * i + 1];
            maxs[i] = Math.max(maxs[2 * i], maxs[2 * i + 1]);

            {
                int[] L = vasc[2 * i], R = vdesc[2 * i + 1];
                int[] LP = pasc[2 * i], RP = pdesc[2 * i + 1];
                int k = 0;
                for (int j = 0; j < L.length; j++) {
                    while (k < R.length && R[k] >= L[j]) {
                        k++;
                    }
                    if (k == 0) continue;
                    int right = RP[k - 1];
                    int left = LP[j];
                    long val = (long) (left + right + 3) * L[j];
//					tr(L, R, LP, RP, left, right, val);
                    maxs[i] = Math.max(maxs[i], val);
                }
            }
            {
                int[] R = vasc[2 * i], L = vdesc[2 * i + 1];
                int[] RP = pasc[2 * i], LP = pdesc[2 * i + 1];
                int k = 0;
                for (int j = 0; j < L.length; j++) {
                    while (k < R.length && R[k] >= L[j]) {
                        k++;
                    }
                    if (k == 0) continue;
                    int right = RP[k - 1];
                    int left = LP[j];
                    long val = (long) (left + right + 3) * L[j];
                    maxs[i] = Math.max(maxs[i], val);
                }
            }
        }

        public static int[] rev(int[] a) {
            int[] b = new int[a.length];
            for (int i = 0; i < a.length; i++) b[a.length - 1 - i] = a[i];
            return b;
        }


        public void update(int pos, int v) {
            vasc[half + pos][0] = v;
            vdesc[half + pos][0] = v;
            maxs[half + pos] = vasc[half + pos][0] * 2;
            for (int i = half + pos >>> 1; i >= 1; i >>>= 1) {
                propagate(i);
            }
        }

        public long max(int l, int r) {
            gmax = Long.MIN_VALUE;
            max(l, r, 0, half, 1);
            return gmax;
        }

        long gmax;

        private int[][] max(int l, int r, int cl, int cr, int cur) {
            if (l <= cl && cr <= r) {
                gmax = Math.max(gmax, maxs[cur]);
                return new int[][]{vasc[cur], pasc[cur], vdesc[cur], pdesc[cur]};
            } else {
                int mid = cl + cr >>> 1;
                int[][] LX = null, RX = null;
                if (cl < r && l < mid) {
                    LX = max(l, r, cl, mid, 2 * cur);
                }
                if (mid < r && l < cr) {
                    RX = max(l, r, mid, cr, 2 * cur + 1);
                }

                if (LX == null) return RX;
                if (RX == null) return LX;

                int[][] ret = new int[4][];
                int[][] res = merge(LX[0], LX[1], RX[0], RX[1]);
                ret[0] = res[0];
                ret[1] = res[1];

                res = merge(RX[2], RX[3], LX[2], LX[3]);
                ret[2] = res[0];
                ret[3] = res[1];

                {
                    int[] L = LX[0], R = RX[2];
                    int[] LP = LX[1], RP = RX[3];
                    int k = 0;
                    for (int j = 0; j < L.length; j++) {
                        while (k < R.length && R[k] >= L[j]) {
                            k++;
                        }
                        if (k == 0) continue;
                        int right = RP[k - 1];
                        int left = LP[j];
                        long val = (long) (left + right + 3) * L[j];
//						tr(L, R, LP, RP, left, right, L, val);
                        gmax = Math.max(gmax, val);
                    }
                }
                {
                    int[] R = LX[0], L = RX[2];
                    int[] RP = LX[1], LP = RX[3];
                    int k = 0;
                    for (int j = 0; j < L.length; j++) {
                        while (k < R.length && R[k] >= L[j]) {
                            k++;
                        }
                        if (k == 0) continue;
                        int right = RP[k - 1];
                        int left = LP[j];
                        long val = (long) (left + right + 3) * L[j];
                        gmax = Math.max(gmax, val);
                    }
                }
                return ret;
            }
        }
    }


    private static int lcp(String s, String s1) {
        int m = 0;
        for (int i = 0; i < Math.min(s.length(), s1.length()); i++) {
            if (s.charAt(i) != s1.charAt(i)) break;
            m++;
        }
        return m;
    }

    private static void solveT() throws IOException {
        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    }


    private static long gcd(long l, long l1) {
        if (l > l1) return gcd(l1, l);
        if (l == 0) return l1;
        return gcd(l1 % l, l);
    }

    private static long pow(long a, long b, long m) {
        if (b == 0) return 1;
        if (b == 1) return a;
        long pp = pow(a, b / 2, m);
        pp *= pp;
        pp %= m;
        return (pp * (b % 2 == 0 ? 1 : a)) % m;
    }


    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner(BufferedReader br) {
            this.br = br;
        }

        public MyScanner(InputStream in) {
            this(new BufferedReader(new InputStreamReader(in)));
        }

        void findToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
        }

        String next() {
            findToken();
            return st.nextToken();
        }

        Integer[] nab(int n) {
            Integer[] k = new Integer[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        int[] na(int n) {
            int[] k = new int[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        long[] nl(int n) {
            long[] k = new long[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.nextLong();
            }
            return k;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int fi() {
            String t = next();
            int cur = 0;
            boolean n = t.charAt(0) == '-';
            for (int a = n ? 1 : 0; a < t.length(); a++) {
                cur = cur * 10 + t.charAt(a) - '0';
            }
            return n ? -cur : cur;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    private static final class STree {
        private final boolean maxt;
        int rs;
        int[] val1;
        int[] from1;
        int[] to1;
        int[] metric;

        public STree(int c, boolean maxt) {
            rs = c;
            this.maxt = maxt;
            int size = Integer.highestOneBit(c);
            if (size != c) {
                size <<= 1;
            }
            int rs = size << 1;
            val1 = new int[rs];
            from1 = new int[rs];
            metric = new int[rs];
            to1 = new int[rs];

            Arrays.fill(from1, Integer.MAX_VALUE);
            if (!maxt)
                Arrays.fill(metric, Integer.MAX_VALUE);
            for (int r = rs - 1; r > 1; r--) {
                if (r >= size) {
                    from1[r] = r - size;
                    to1[r] = r - size;
                }
                from1[r / 2] = Math.min(from1[r / 2], from1[r]);
                to1[r / 2] = Math.max(to1[r / 2], to1[r]);
            }
        }

        public STree(int c) {
            this(c, true);
        }

        public int max(int from, int to) {
            return max(1, from, to);
        }

        private int max(int cur, int from, int to) {
            if (cur >= val1.length) return 0;
            if (from <= from1[cur] && to1[cur] <= to) {
                return metric[cur];
            }
            if (from1[cur] > to || from > to1[cur]) {
                return 0;
            }
            cur <<= 1;
            return Math.max(max(cur, from, to), max(cur + 1, from, to));
        }


        public void put(int x, int val) {
            x += val1.length >> 1;
            val1[x] = val;
            metric[x] = val;
            addToParent(x);
        }


        private void addToParent(int cur) {
            while (cur > 1) {
                cur >>= 1;
                if (maxt) {
                    metric[cur] = Math.max(metric[cur << 1], metric[1 + (cur << 1)]);
                } else {
                    metric[cur] = Math.min(metric[cur << 1], metric[1 + (cur << 1)]);
                }

            }
        }

        public long x(int i) {
            return val1[i + val1.length >> 1];
        }
    }
}