Problem: There are n cells, numbered 1,2,..., n from left to right. You have to place a robot at any cell initially. The robot must make exactly k moves.

In one move, the robot must move one cell to the left or right, provided that it doesn't move out of bounds. In other words, if the robot was in the cell i, it must move to either the cell i-1 or the cell i+1, as long as it lies between 1 and n (endpoints inclusive). The cells, in the order they are visited (including the cell the robot is placed), together make a good path.

Each cell i has a value a_i associated with it. Let c_0, c_1, ..., c_k be the sequence of cells in a good path in the order they are visited (c_0 is the cell robot is initially placed, c_1 is the cell where the robot is after its first move, and so on; more formally, c_i is the cell that the robot is at after i moves). Then the value of the path is calculated as a_{c_0} + a_{c_1} + ... + a_{c_k}.

Your task is to calculate the sum of values over all possible good paths. Since this number can be very large, output it modulo 10^9 + 7. Two good paths are considered different if the starting cell differs or there exists an integer i ∈ [1, k] such that the current cell of the robot after exactly i moves is different in those paths.

You must process q updates to a and print the updated sum each time. Each update changes the value of exactly one cell. See the input format and the sample input-output for more details.

Input

The first line of the input contains three space-separated integers n, k and q (2 ≤ n ≤ 5000; 1 ≤ k ≤ 5000; 1 ≤ q ≤ 2 ⋅ 10^5).

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

q lines follow. Each line contains two space-separated integers i and x (1 ≤ i ≤ n; 1 ≤ x ≤ 10^9) indicating that you must change the value of a_i to x.

Output

Print q integers. The i-th integer should be the sum of values over all good paths after the first i updates are performed. Since the answers may be large, print them modulo 10^9 + 7.

Examples

Input


5 1 5
3 5 1 4 2
1 9
2 4
3 6
4 6
5 2


Output


62
58
78
86
86


Input


5 2 5
3 5 1 4 2
1 9
2 4
3 6
4 6
5 2


Output


157
147
207
227
227


Input


4 40 6
92 21 82 46
3 56
1 72
4 28
1 97
2 49
2 88


Output


239185261
666314041
50729936
516818968
766409450
756910476

Note

In the first example, the good paths are (1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3), (4, 5), (5, 4).

Initially the values of a are [3, 5, 1, 4, 2]. After the first update, they become [9, 5, 1, 4, 2]. After the second update, they become [9, 4, 1, 4, 2], and so on.

Solution (in JAVA):

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

public class Main {
    static PrintWriter pw;
    static Scanner sc;
    static long ceildiv(long x, long y) { return (x+y-1)/y; }
    static int mod(long x, int m) { return (int)((x%m+m)%m); }
    static void put(TreeMap<Pair, Integer> map, Pair p){if(map.containsKey(p)) map.replace(p, map.get(p)+1); else map.put(p, 1); }
    static void rem(TreeMap<Pair, Integer> map, Pair p){ if(map.get(p)==1) map.remove(p);else map.replace(p, map.get(p)-1); }
    static void printf(double x, int dig){ String s="%."+dig+"f"; pw.printf(s, x); }
    static int Int(boolean x){ return x?1:0; }
    static final int inf=(int)1e9, mod=inf+7;
    static final long infL=inf*1l*inf;
    static final double r2=Math.sqrt(2), eps=1e-9;
    public static long gcd(long x, long y) { return y==0? x: gcd(y, x%y); }
    public static void main(String[] args) throws IOException{
        sc=new Scanner(System.in);
        pw=new PrintWriter(System.out);
//        int t=sc.nextInt();
//        while(t-->0)
            testcase();
        pw.close();
    }
    static int[] arr;
    static long[] dp[];
    static void testcase() throws IOException{
        int n=sc.nextInt(), k=sc.nextInt(), q=sc.nextInt();
        int[] arr=sc.nextArr(n);
        dp=new long[n][k+1];
        for (int i = 0; i < n; i++)
            Arrays.fill(dp[i], -1);
        long[] cnt=new long[n];;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < k+1; j++)
                cnt[i]=(cnt[i]+(solve(i, j)*solve(i, k-j))%mod)%mod;
        }
        long ans=0;
        for (int i = 0; i < n; i++)
            ans=(ans+cnt[i]*arr[i])%mod;
        while(q-->0){
            int idx=sc.nextInt()-1, val=sc.nextInt();
            int diff=val-arr[idx];
            arr[idx]=val;
            ans=mod(ans+diff*cnt[idx], mod);
            pw.println(ans);
        }
    }
    static long solve(int idx, int rem){
        if(idx==-1 || idx== dp.length)
            return 0;
        if(rem==dp[idx].length-1)
            return 1;
        if(dp[idx][rem]!=-1)
            return dp[idx][rem];
        return dp[idx][rem]=(solve(idx-1, rem+1)+solve(idx+1, rem+1))%mod;
    }
    static void printArr(int[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(long[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(double[] arr) {
        for (int i = 0; i < arr.length - 1; i++)
            pw.print(arr[i] + " ");
        pw.println(arr[arr.length - 1]);
    }
    static void printArr(Integer[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(ArrayList<Integer> list) {
        for (int i = 0; i < list.size(); i++)
            pw.print(list.get(i)+" ");
        pw.println();
    }
    static void printArr(boolean[] arr) {
        StringBuilder sb=new StringBuilder();
        for(boolean b: arr)
            sb.append(Int(b));
        pw.println(sb.toString());
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public int[] nextDigits() throws IOException{
            String s=nextLine();
            int[] arr=new int[s.length()];
            for(int i=0; i<arr.length; i++)
                arr[i]=s.charAt(i)-'0';
            return arr;
        }
        public int[] nextArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < arr.length; i++)
                arr[i] = nextInt();
            return arr;
        }
        public Integer[] nextsort(int n) throws IOException{
            Integer[] arr=new Integer[n];
            for(int i=0; i<n; i++)
                arr[i]=nextInt();
            return arr;
        }
        public Pair nextPair() throws IOException{
            return new Pair(nextInt(), nextInt());
        }
        public Pair[] nextPairArr(int n) throws IOException{
            Pair[] arr=new Pair[n];
            for(int i=0; i<n; i++)
                arr[i]=nextPair();
            return arr;
        }
        public boolean ready() throws IOException {
            return br.ready();
        }
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
        public boolean contains(int a){
            return x==a || y==a;
        }
        public int hashCode() {
            return (this.x*1000000000+this.y);
        }
        public int compareTo(Pair p){
            if(x==p.x)
                return y-p.y;
            return x-p.x;
        }
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (this.getClass() != obj.getClass()) {
                return false;
            }
            Pair p = (Pair) obj;
            return this.x==p.x && this.y==p.y;
        }
        public Pair clone(){
            return new Pair(x, y);
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public void add(Pair p){
            x+=p.x;
            y+=p.y;
        }
        public Pair negative(){
            return new Pair(-x, -y);
        }
    }
    static class LP implements Comparable<LP>{
        long x, y;
        public LP(long a, long b){
            x=a;
            y=b;
        }
        public void add(LP p){
            x+=p.x;
            y+=p.y;
        }
        public boolean equals(LP p){
            return p.x==x && y==p.y;
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public int compareTo(LP p){
            int a=Long.compare(x, p.x);
            if(a!=0)
                return a;
            return Long.compare(y, p.y);
        }
    }
    static class Triple implements Comparable<Triple>{
        int x, y, z;
        public Triple(int a, int b, int c){
            x=a;
            y=b;
            z=c;
        }
        public int compareTo(Triple t){
            if(this.y!=t.y)
                return y-t.y;
            return x-t.x;
        }
        public String toString(){
            return x+" "+y+" "+z;
        }
    }
}