Buber is a Berland technology company that specializes in waste of investor's money. Recently Buber decided to transfer its infrastructure to a cloud. The company decided to rent CPU cores in the cloud for n consecutive days, which are numbered from 1 to n. Buber requires k CPU cores each day.

The cloud provider offers m tariff plans, the i-th tariff plan is characterized by the following parameters:

  * l_i and r_i — the i-th tariff plan is available only on days from l_i to r_i, inclusive, 
  * c_i — the number of cores per day available for rent on the i-th tariff plan, 
  * p_i — the price of renting one core per day on the i-th tariff plan. 



Buber can arbitrarily share its computing core needs between the tariff plans. Every day Buber can rent an arbitrary number of cores (from 0 to c_i) on each of the available plans. The number of rented cores on a tariff plan can vary arbitrarily from day to day.

Find the minimum amount of money that Buber will pay for its work for n days from 1 to n. If on a day the total number of cores for all available tariff plans is strictly less than k, then this day Buber will have to work on fewer cores (and it rents all the available cores), otherwise Buber rents exactly k cores this day.

Input

The first line of the input contains three integers n, k and m (1 ≤ n,k ≤ 10^6, 1 ≤ m ≤ 2⋅10^5) — the number of days to analyze, the desired daily number of cores, the number of tariff plans.

The following m lines contain descriptions of tariff plans, one description per line. Each line contains four integers l_i, r_i, c_i, p_i (1 ≤ l_i ≤ r_i ≤ n, 1 ≤ c_i, p_i ≤ 10^6), where l_i and r_i are starting and finishing days of the i-th tariff plan, c_i — number of cores, p_i — price of a single core for daily rent on the i-th tariff plan.

Output

Print a single integer number — the minimal amount of money that Buber will pay.

Examples

Input

5 7 3
1 4 5 3
1 3 5 2
2 5 10 1


Output

44


Input

7 13 5
2 3 10 7
3 5 10 10
1 2 10 6
4 5 10 9
3 4 10 8


Output

462


Input

4 100 3
3 3 2 5
1 1 3 2
2 4 4 4


Output

64
import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;

public class ac {
    private static final int N = 1000100;
    static long[]S=new long[N<<2];
    static long[]sum=new long[N<<2];
    static long ans;
    static ArrayList<long[]>[]U=new ArrayList[N];
    static void update(int t,int l,int r,long c,long p){
        S[t]+=c;sum[t]+=c*p;
        if (l==r)return;
        int mid=l+r>>1;
        if (p<=mid)update(t<<1,l,mid,c,p);
        else update(t<<1|1,mid+1,r,c,p);
    }

    static long query(int t,int l,int r,long k){
        if (k<=0)return 0;
        if (S[t]<=k)return sum[t];
        if (l==r)return k*l;
        int mid=l+r>>1;
        return query(t<<1,l,mid,k)+query(t<<1|1,mid+1,r,k-S[t<<1]);
    }

    public static void main(String[] args) {
        for (int i = 0; i < U.length; i++) U[i]=new ArrayList<>();
        IO io=new IO();
        int n=io.nextInt(),k=io.nextInt(),m=io.nextInt();
        for (int i = 0; i <m ; i++) {
            int l=io.nextInt(),r=io.nextInt(),c=io.nextInt(),p=io.nextInt();
            U[l].add(new long[]{c,p});
            U[r+1].add(new long[]{-c,p});
        }
        for (int i=1;i<=n;i++){
            for (int j = 0; j < U[i].size(); j++) {
                update(1,1,N,U[i].get(j)[0],U[i].get(j)[1]);
            }
            ans+=query(1,1,N,Math.min(S[1],k));
        }
        io.println(ans);
    }

    static class IO {

        BufferedInputStream din;
        final int BUFFER_SIZE = 1 << 16;
        byte[] buffer;
        int byteRead, bufferPoint;

        StringBuilder builder;
        PrintWriter pw;

        public IO() {
            din = new BufferedInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPoint = byteRead = 0;

            builder = new StringBuilder();
            pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                    System.out
            )), true);
        }

        int read() {
            if (bufferPoint >= byteRead) {
                try {
                    byteRead = din.read(buffer, bufferPoint = 0, BUFFER_SIZE);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (byteRead == -1) buffer[0] = -1;
            }
            return buffer[bufferPoint++];
        }

        int peek() {
            if (byteRead == -1) return -1;
            if (bufferPoint >= byteRead) {
                try {
                    byteRead = din.read(buffer, bufferPoint = 0, BUFFER_SIZE);
                } catch (IOException e) {
                    return -1;
                }
                if (byteRead <= 0) return -1;
            }
            return buffer[bufferPoint];
        }

        boolean hasNext() {
            int c = peek();
            while (c != -1 && c <= ' ') {
                read();
                c = peek();
            }
            return c != -1;
        }

        char nextChar() {
            int c = read();
            while (c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1) {
                c = read();
            }
            return (char) c;
        }

        double nextDouble() {
            double ret = 0, div = 1;
            int c = read();
            while (c <= ' ')
                c = read();
            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;
        }

        String nextLine() {
            byte[] strBuf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt == 0) {
                        continue;
                    } else {
                        break;
                    }
                }
                if (strBuf.length == cnt) {
                    strBuf = Arrays.copyOf(strBuf, strBuf.length * 2);
                }
                strBuf[cnt++] = (byte) c;
            }
            return new String(strBuf, 0, cnt);
        }


        String next() {
            byte[] strBuf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (Character.isWhitespace(c)) {
                    if (cnt == 0) {
                        continue;
                    } else {
                        break;
                    }
                }
                if (strBuf.length == cnt) {
                    strBuf = Arrays.copyOf(strBuf, strBuf.length * 2);
                }
                strBuf[cnt++] = (byte) c;
            }
            return new String(strBuf, 0, cnt);
        }

        int nextInt() {
            int ans = 0;
            int c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ans = ans * 10 + c - '0';
            } while ('0' <= (c = read()) && c <= '9');
            bufferPoint--;
            return neg ? -ans : ans;
        }

        long nextLong() {
            long ans = 0;
            int c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ans = ans * 10 + c - '0';
            } while ('0' <= (c = read()) && c <= '9');
            bufferPoint--;
            return neg ? -ans : ans;
        }

        void println(Object o) {
            pw.println(o);
        }

        void print(Object o) {
            pw.print(o);
        }

        void printf(String format, Object... objects) {
            pw.printf(format, objects);
        }

        void close() {
            pw.close();
        }

        void done(Object o) {
            print(o);
            close();
        }

    }

}
