Sasha is a very happy guy, that's why he is always on the move. There are n cities in the country where Sasha lives. They are all located on one straight line, and for convenience, they are numbered from 1 to n in increasing order. The distance between any two adjacent cities is equal to 1 kilometer. Since all roads in the country are directed, it's possible to reach the city y from the city x only if x < y. 

Once Sasha decided to go on a trip around the country and to visit all n cities. He will move with the help of his car, Cheetah-2677. The tank capacity of this model is v liters, and it spends exactly 1 liter of fuel for 1 kilometer of the way. At the beginning of the journey, the tank is empty. Sasha is located in the city with the number 1 and wants to get to the city with the number n. There is a gas station in each city. In the i-th city, the price of 1 liter of fuel is i dollars. It is obvious that at any moment of time, the tank can contain at most v liters of fuel.

Sasha doesn't like to waste money, that's why he wants to know what is the minimum amount of money is needed to finish the trip if he can buy fuel in any city he wants. Help him to figure it out!

Input

The first line contains two integers n and v (2 ≤ n ≤ 100, 1 ≤ v ≤ 100) — the number of cities in the country and the capacity of the tank.

Output

Print one integer — the minimum amount of money that is needed to finish the trip.

Examples

Input


4 2


Output


4


Input


7 6


Output


6

Note

In the first example, Sasha can buy 2 liters for 2 dollars (1 dollar per liter) in the first city, drive to the second city, spend 1 liter of fuel on it, then buy 1 liter for 2 dollars in the second city and then drive to the 4-th city. Therefore, the answer is 1+1+2=4.

In the second example, the capacity of the tank allows to fill the tank completely in the first city, and drive to the last city without stops in other cities.
// package Practice.CF1113;

import java.io.*;
import java.util.*;


public class CF1113A {
    static FastReader s;
    static PrintWriter out;
    static String INPUT = "4 2\n";

    public static void main(String[] args) {
        long time = System.currentTimeMillis();
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        out = new PrintWriter(System.out);
        s = new FastReader(oj);

        int n = s.nextInt();
        int v = s.nextInt();

        int totalMoneySpent = Math.min(v, n - 1);
        for (int i = 1; i < n - v; i++) {
            if(i  + v == n - 1) {
                totalMoneySpent += (i+1);
                break;
            } else {
                totalMoneySpent += (i+1);
            }
        }
        out.println(totalMoneySpent);
        
        if (!oj) {
            System.out.println(Arrays.deepToString(new Object[]{System.currentTimeMillis() - time + " ms"}));
        }
        out.flush();
    }


    private static class Maths {
        static ArrayList<Long> printDivisors(long n) {
            // Note that this loop runs till square root
            ArrayList<Long> list = new ArrayList<>();
            for (long i = 1; i <= Math.sqrt(n); i++) {
                if (n % i == 0) {
                    if (n / i == i) {
                        list.add(i);
                    } else {
                        list.add(i);
                        list.add(n / i);
                    }
                }
            }
            return list;
        }


        //    GCD - Using Euclid theorem.
        private static long gcd(long a, long b) {
            if (b == 0) {
                return a;
            }

            return gcd(b, a % b);
        }

        //    Extended euclidean algorithm
//    Used to solve equations of the form ax + by = gcd(a,b)
//    return array [d, a, b] such that d = gcd(p, q), ap + bq = d
        static long[] extendedEuclidean(long p, long q) {
            if (q == 0)
                return new long[]{p, 1, 0};

            long[] vals = extendedEuclidean(q, p % q);
            long d = vals[0];
            long a = vals[2];
            long b = vals[1] - (p / q) * vals[2];
            return new long[]{d, a, b};
        }

        // X ^ y mod p
        static long power(long x, long y, long p) {
            long res = 1;
            x = x % p;

            while (y > 0) {
                if ((y & 1) == 1)
                    res = (res * x) % p;
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }

        // Returns modulo inverse of a
        // with respect to m using extended
        // Euclid Algorithm. Refer below post for details:
        // https://www.geeksforgeeks.org/multiplicative-inverse-under-modulo-m/
        static long inv(long a, long m) {
            long m0 = m, t, q;
            long x0 = 0, x1 = 1;

            if (m == 1)
                return 0;

            // Apply extended Euclid Algorithm
            while (a > 1) {
                q = a / m;
                t = m;
                m = a % m;
                a = t;
                t = x0;
                x0 = x1 - q * x0;
                x1 = t;
            }

            // Make x1 positive
            if (x1 < 0)
                x1 += m0;

            return x1;
        }

        // k is size of num[] and rem[].
        // Returns the smallest number
        // x such that:
        // x % num[0] = rem[0],
        // x % num[1] = rem[1],
        // ..................
        // x % num[k-2] = rem[k-1]
        // Assumption: Numbers in num[] are pairwise
        // coprime (gcd for every pair is 1)
        static long findMinX(long num[], long rem[], long k) {
            int prod = 1;
            for (int i = 0; i < k; i++)
                prod *= num[i];

            int result = 0;
            for (int i = 0; i < k; i++) {
                long pp = prod / num[i];
                result += rem[i] * inv(pp, num[i]) * pp;
            }

            return result % prod;
        }
    }

    private static class BS {
        //  Binary search
        private static int binarySearch(int[] arr, int ele) {
            int low = 0;
            int high = arr.length - 1;
            while (low <= high) {
                int mid = (low + high) / 2;
                if (arr[mid] == ele) {
                    return mid;
                } else if (ele < arr[mid]) {
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            return -1;
        }

        //    First occurence using binary search
        private static int binarySearchFirstOccurence(int[] arr, int ele) {
            int low = 0;
            int high = arr.length - 1;
            int ans = -1;
            while (low <= high) {
                int mid = (low + high) / 2;
                if (arr[mid] == ele) {
                    ans = mid;
                    high = mid - 1;
                } else if (ele < arr[mid]) {
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            return ans;
        }


        //    Last occurenece using binary search
        private static int binarySearchLastOccurence(int[] arr, int ele) {
            int low = 0;
            int high = arr.length - 1;
            int ans = -1;
            while (low <= high) {
                int mid = (low + high) / 2;
                if (arr[mid] == ele) {
                    ans = mid;
                    low = mid + 1;
                } else if (ele < arr[mid]) {
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            return ans;
        }
    }

    private static class arrays {
        // Merge sort
        static void merge(int arr[], int l, int m, int r) {
            int n1 = m - l + 1;
            int n2 = r - m;
            int L[] = new int[n1];
            int R[] = new int[n2];
            for (int i = 0; i < n1; ++i)
                L[i] = arr[l + i];
            for (int j = 0; j < n2; ++j)
                R[j] = arr[m + 1 + j];
            int i = 0, j = 0;
            int k = l;
            while (i < n1 && j < n2) {
                if (L[i] <= R[j]) {
                    arr[k] = L[i];
                    i++;
                } else {
                    arr[k] = R[j];
                    j++;
                }
                k++;
            }

            while (i < n1) {
                arr[k] = L[i];
                i++;
                k++;
            }

            while (j < n2) {
                arr[k] = R[j];
                j++;
                k++;
            }
        }

        static void sort(int arr[], int l, int r) {
            if (l < r) {
                int m = (l + r) / 2;
                sort(arr, l, m);
                sort(arr, m + 1, r);
                merge(arr, l, m, r);
            }
        }

        static void sort(int[] arr) {
            sort(arr, 0, arr.length - 1);
        }
    }

    private static class UnionFindDisjointSet {
        int[] parent;
        int[] size;
        int n;
        int size1;

        public UnionFindDisjointSet(int n) {
            this.n = n;
            this.parent = new int[n];
            this.size = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }

            for (int i = 0; i < n; i++) {
                size[i] = 1;
            }

            this.size1 = n;
        }

        private int numDisjointSets() {
            System.out.println(size1);
            return size1;
        }

        private boolean find(int a, int b) {
            int rootA = root(a);
            int rootB = root(b);
            if (rootA == rootB) {
                return true;
            }
            return false;
        }

        private int root(int b) {
            while (parent[b] != b) {
                parent[b] = parent[parent[b]];
                b = parent[b];
            }
            return b;
        }

        private void union(int a, int b) {
            int rootA = root(a);
            int rootB = root(b);
            if (rootA == rootB) {
                return;
            }

            if (size[rootA] < size[rootB]) {
                parent[rootA] = parent[rootB];
                size[rootB] += size[rootA];
            } else {
                parent[rootB] = parent[rootA];
                size[rootA] += size[rootB];
            }
            size1--;
            System.out.println(Arrays.toString(parent));
        }
    }

    private static class SegTree {
        int[] st;
        int[] arr;

        public SegTree(int[] arr) {
            this.arr = arr;
            int size = (int) Math.ceil(Math.log(arr.length) / Math.log(2));
            st = new int[(int) ((2 * Math.pow(2, size)) - 1)];
            buildSegmentTree(1, 0, arr.length - 1);
        }

        //**********JUST CALL THE CONSTRUCTOR, THIS FUNCTION WILL BE CALLED AUTOMATICALLY******
        private void buildSegmentTree(int index, int L, int R) {
            if (L == R) {
                st[index] = arr[L];
                return;
            }

            buildSegmentTree(index * 2, L, (L + R) / 2);
            buildSegmentTree(index * 2 + 1, (L + R) / 2 + 1, R);
//          Replace this line if you want to change the function of the Segment tree.
            st[index] = Math.min(st[index * 2], st[index * 2 + 1]);
        }

        //***********We have to use this function **************
        private int Query(int queL, int queR) {
            return Query1(1, 0, arr.length - 1, queL, queR);
        }

        //This is a helper function.
        //************* DO NOT USE THIS ****************
        private int Query1(int index, int segL, int segR, int queL, int queR) {
            if (queL > segR || queR < segL) {
                return -1;
            }

            if (queL <= segL && queR >= segR) {
                return st[index];
            }

            int ans1 = Query1(index * 2, segL, (segL + segR) / 2, queL, queR);
            int ans2 = Query1(index * 2 + 1, (segL + segR) / 2 + 1, segR, queL, queR);
            if (ans1 == -1) {
                return ans2;
            }

            if (ans2 == -1) {
                return ans1;
            }
//             Segment tree implemented for range minimum query. Change the below line to change the function.
            return Math.min(ans1, ans2);
        }

        private void update(int idx, int val) {
            update1(1, 0, arr.length - 1, idx, val);
        }

        private void update1(int node, int queL, int queR, int idx, int val) {
            // idx - index to be updated in the array
            // node - index to be updated in the seg tree
            if (queL == queR) {
                // Leaf node
                arr[idx] += val;
                st[node] += val;
            } else {
                int mid = (queL + queR) / 2;
                if (queL <= idx && idx <= mid) {
                    // If idx is in the left child, recurse on the left child
                    update1(2 * node, queL, mid, idx, val);
                } else {
                    // if idx is in the right child, recurse on the right child
                    update1(2 * node + 1, mid + 1, queR, idx, val);
                }
                // Internal node will have the min of both of its children
                st[node] = Math.min(st[2 * node], st[2 * node + 1]);
            }
        }

    }

    private static class FastReader {
        InputStream is;

        public FastReader(boolean onlineJudge) {
            is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        }

        byte[] inbuf = new byte[1024];
        public int lenbuf = 0, ptrbuf = 0;

        int readByte() {
            if (lenbuf == -1)
                throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0)
                    return -1;
            }
            return inbuf[ptrbuf++];
        }

        boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b))
                ;
            return b;
        }

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

        char nextChar() {
            return (char) skip();
        }

        String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        String nextLine() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while ((!isSpaceChar(b) || b == ' ')) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
                ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
                ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        char[][] nextMatrix(int n, int m) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++)
                map[i] = next(m);
            return map;
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        int[][] next2DInt(int n, int m) {
            int[][] arr = new int[n][];
            for (int i = 0; i < n; i++) {
                arr[i] = nextIntArray(m);
            }
            return arr;
        }

        long[][] next2DLong(int n, int m) {
            long[][] arr = new long[n][];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLongArray(m);
            }
            return arr;
        }

        int[] shuffle(int[] arr) {
            Random r = new Random();
            for (int i = 1, j; i < arr.length; i++) {
                j = r.nextInt(i);
                arr[i] = arr[i] ^ arr[j];
                arr[j] = arr[i] ^ arr[j];
                arr[i] = arr[i] ^ arr[j];
            }
            return arr;
        }

        int[] uniq(int[] arr) {
            Arrays.sort(arr);
            int[] rv = new int[arr.length];
            int pos = 0;
            rv[pos++] = arr[0];
            for (int i = 1; i < arr.length; i++) {
                if (arr[i] != arr[i - 1]) {
                    rv[pos++] = arr[i];
                }
            }
            return Arrays.copyOf(rv, pos);
        }
    }

}
