Problem: As we all know, Dart is some kind of creature from Upside Down world. For simplicity, we call their kind pollywogs. Dart and x - 1 other pollywogs are playing a game. There are n stones in a row, numbered from 1 through n from left to right. At most 1 pollywog may be sitting on each stone at a time. Initially, the pollywogs are sitting on the first x stones (one pollywog on each stone).

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Dart and his friends want to end up on the last x stones. At each second, the leftmost pollywog should jump to the right. A pollywog can jump at most k stones; more specifically, a pollywog can jump from stone number i to stones i + 1, i + 2, ... i + k. A pollywog can't jump on an occupied stone. Jumping a distance i takes ci amounts of energy from the pollywog. 

Also, q stones are special Each time landing on a special stone p, takes wp amounts of energy (in addition to the energy for jump) from the pollywog. wp could be negative, in this case, it means the pollywog absorbs |wp| amounts of energy.

Pollywogs want to spend as little energy as possible (this value could be negative). 

They're just pollywogs, so they asked for your help. Tell them the total change in their energy, in case they move optimally.

Input

The first line of input contains four integers, x, k, n and q (1 ≤ x ≤ k ≤ 8, k ≤ n ≤ 108, 0 ≤ q ≤ min(25, n - x)) — the number of pollywogs, the maximum length of jump, the number of stones and the number of special stones.

The next line contains k integers, c1, c2, ... ck, separated by spaces (1 ≤ ci ≤ 109) — the energetic costs of jumps.

The next q lines contain description of the special stones. Each line contains two integers p and wp (x + 1 ≤ p ≤ n, |wp| ≤ 109). All p are distinct.

Output

Print the minimum amount of energy they need, in the first and only line of output.

Examples

Input

2 3 10 2
1 2 3
5 -10
6 1000


Output

6


Input

4 7 85 3
17 5 28 4 52 46 6
59 -76
33 -69
19 2018


Output

135

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public int x;
        public int k;
        public int n;
        public int q;
        public int[] c;
        public int[] idxtostate;
        public int[] statetoidx;
        public long INF = 1L << 61;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            x = in.nextInt();
            k = in.nextInt();
            n = in.nextInt();
            q = in.nextInt();
            c = in.readIntArray(k);
            TaskC.Stone[] ss = new TaskC.Stone[q + 1];
            for (int i = 0; i < q; i++) ss[i] = new TaskC.Stone(in.nextInt() - 1, in.nextInt());
            ss[q] = new TaskC.Stone(n, 0);
            Arrays.sort(ss, Comparator.comparingInt(ww -> ww.p));
            statetoidx = new int[1 << k];
            idxtostate = new int[1 << k];
            int id = 0;
            for (int i = 0; i < 1 << k; i++) {
                if (Integer.bitCount(i) == x) {
                    statetoidx[i] = id;
                    idxtostate[id] = i;
                    id++;
                }
            }
            long[][][] basepow = new long[60][id][id];
            AUtils.deepFill(basepow, INF);
            for (int i = 0; i < id; i++) {
                int state = idxtostate[i];
                if (((state >> (k - 1)) & 1) == 0) {
                    basepow[0][statetoidx[state]][statetoidx[state << 1]] = 0;
                    continue;
                }
                for (int jump = 1; jump <= k; jump++) {
                    int nstate = state - (1 << (k - 1));
                    nstate <<= 1;
                    if (((nstate >> (k - jump)) & 1) == 1) continue;
                    basepow[0][statetoidx[state]][statetoidx[nstate | (1 << (k - jump))]] = c[jump - 1];
                }
            }
            for (int level = 1; level < basepow.length; level++) {
                basepow[level] = mult(basepow[level - 1], basepow[level - 1]);
            }

            long[][] cost = new long[id][id];
            AUtils.deepFill(cost, INF);
            int ttt = (1 << k) - (1 << (k - x));
            cost[statetoidx[ttt]][statetoidx[ttt]] = 0;

            int cpos = 0;
            int sidx = 0;
            while (cpos < n - x) {
                while (cpos > ss[sidx].p) sidx++;
                if (cpos + k >= ss[sidx].p) {
                    long[][] base = new long[id][id];
                    AUtils.deepFill(base, INF);
                    for (int i = 0; i < id; i++) {
                        int state = idxtostate[i];
                        if (((state >> (k - 1)) & 1) == 0) {
                            base[statetoidx[state]][statetoidx[state << 1]] = 0;
                            continue;
                        }
                        for (int jump = 1; jump <= k; jump++) {
                            int nstate = state - (1 << (k - 1));
                            nstate <<= 1;
                            if (((nstate >> (k - jump)) & 1) == 1) continue;
                            int tcost = c[jump - 1];
                            for (int a = 0; a < 2*k; a++) {
                                if (sidx + a < ss.length && cpos + jump == ss[sidx + a].p) {
                                    tcost += ss[sidx + a].w;
                                }
                            }
                            base[statetoidx[state]][statetoidx[nstate | (1 << (k - jump))]] = tcost;
                        }
                    }
                    cost = mult(cost, base);
                    cpos++;
                } else {
                    long need = (ss[sidx].p - k - cpos);
                    for (int j = 0; j < 60; j++) {
                        if (((need >> j) & 1) == 1) {
                            cost = mult(cost, basepow[j]);
                        }
                    }
                    cpos += need;
                }
            }

            out.println(cost[statetoidx[ttt]][statetoidx[ttt]]);
        }

        public long[][] mult(long[][] a, long[][] b) {
            int n = a.length;
            long[][] ret = new long[n][n];
            AUtils.deepFill(ret, INF);
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    for (int k = 0; k < n; k++) {
                        ret[i][j] = Math.min(ret[i][j], a[i][k] + b[k][j]);
                    }
                }
            }
            return ret;
        }

        static class Stone {
            public int p;
            public int w;

            public Stone(int p, int w) {
                this.p = p;
                this.w = w;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int[] readIntArray(int tokens) {
            int[] ret = new int[tokens];
            for (int i = 0; i < tokens; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class AUtils {
        public static void deepFill(long[][][] x, long val) {
            for (long[][] y : x) deepFill(y, val);
        }

        public static void deepFill(long[][] x, long val) {
            for (long[] y : x) deepFill(y, val);
        }

        public static void deepFill(long[] x, long val) {
            Arrays.fill(x, val);
        }

    }
}