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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;


public class Main{

    static long MOD = 1_000_000_007L;
    //static long MOD = 998_244_353L;
    //static long MOD = 1_000_000_033L;
    static long [] fac;
    static long [] pow;
    static long [] inv;
    static int[][] dir = new int[][]{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
    static long lMax = 0x3f3f3f3f3f3f3f3fL;
    static int iMax = 0x3f3f3f3f;
    static HashMap <Long, Long> memo = new HashMap();
    static HashMap <Long, Long> memof = new HashMap();
    static HashMap <Long, Long> memogL = new HashMap();
    static HashMap <Long, Long> memogR = new HashMap();
    static MyScanner sc = new MyScanner();
    //static ArrayList <Integer> primes;

    static long[] pow2;
    public static void main(String[] args) {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        // Start writing your solution here. -------------------------------------


        int nn = 300000;

        /*fac = new long[nn + 1];
        fac[1] = 1;
        for(int i = 2; i <= nn; i++)
            fac[i] = fac[i - 1] * 1L * i % MOD;*/

        /*pow = new long[nn + 1];
        pow[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow[i] = pow[i - 1] * 2L % MOD;
        pow[1] = 3L;*/

        /*pow2 = new long[nn + 1];
        pow2[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow2[i] = pow2[i - 1] * 2L % (MOD - 1);*/

        /*inv = new long[nn + 1];
        inv[1] = 1;
        for (int i = 2; i <= nn; ++i)
            inv[i] = (MOD - MOD / i) * inv[(int)(MOD % i)] % MOD;*/

        //primes = sieveOfEratosthenes(100001);


        int t = 1;
        //t = sc.nextInt();


        /*for(int i = 1; i < 1000; i++)
            out.println(i + " " + fam[i]);*/
        while(t-- > 0){
            long[] res = solve();
            for(long i : res) out.println(i);
        }
        out.close();
    }

    static int total = 0;
    static long inv2 = (MOD + 1) / 2;

    static int[] dep;
    static boolean[] vis;

    static long[] solve() {
        /*String s = sc.nextLine();
        char[] c = s.toCharArray();
        int n = c.length;*/
        int n = sc.nextInt();
        int k = sc.nextInt();
        int q = sc.nextInt();
        long a[] = new long[n + 1], sum = 0L;;

        long[] cnt = new long[n + 2];
        long[][] dp = new long[k + 1][n + 2];
        Arrays.fill(dp[0], 1);
        dp[0][0] = dp[0][n + 1] = 0L;
        for(int i = 1; i <= k; i++)
            for(int j = 1; j <= n; j++)
                dp[i][j] = (dp[i - 1][j - 1] + dp[i - 1][j + 1]) % MOD;
        for(int i = 1; i <= n; i++)
            for(int j = 0; j <= k; j++)
                cnt[i] = (cnt[i] + dp[j][i] * dp[k - j][i]) % MOD;
        for(int i = 1; i <= n; i++){
            a[i] = sc.nextLong();
            sum = (sum + cnt[i] * a[i]) % MOD;
        }
        long[] res = new long[q];
        for(int i = 0; i < q; i++){
            int ind = sc.nextInt();
            long tmp = sc.nextLong();
            long diff = tmp - a[ind];
            a[ind] = tmp;
            sum = ((sum + diff * cnt[ind]) % MOD + MOD) % MOD;
            res[i] = sum;
        }
        return res;
    }


    // SegmentTree From uwi
    public class SegmentTreeRMQ {
        public int M, H, N;
        public int[] st;

        public SegmentTreeRMQ(int n)
        {
            N = n;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            Arrays.fill(st, 0, M, Integer.MAX_VALUE);
        }

        public SegmentTreeRMQ(int[] a)
        {
            N = a.length;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            for(int i = 0;i < N;i++){
                st[H+i] = a[i];
            }
            Arrays.fill(st, H+N, M, Integer.MAX_VALUE);
            for(int i = H-1;i >= 1;i--)propagate(i);
        }

        public void update(int pos, int x)
        {
            st[H+pos] = x;
            for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
        }

        private void propagate(int i)
        {
            st[i] = Math.min(st[2*i], st[2*i+1]);
        }

        public int minx(int l, int r){
            int min = Integer.MAX_VALUE;
            if(l >= r)return min;
            while(l != 0){
                int f = l&-l;
                if(l+f > r)break;
                int v = st[(H+l)/f];
                if(v < min)min = v;
                l += f;
            }

            while(l < r){
                int f = r&-r;
                int v = st[(H+r)/f-1];
                if(v < min)min = v;
                r -= f;
            }
            return min;
        }

        public int min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);}

        private int min(int l, int r, int cl, int cr, int cur)
        {
            if(l <= cl && cr <= r){
                return st[cur];
            }else{
                int mid = cl+cr>>>1;
                int ret = Integer.MAX_VALUE;
                if(cl < r && l < mid){
                    ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
                }
                if(mid < r && l < cr){
                    ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
                }
                return ret;
            }
        }

    }


    public static double dist(double a, double b){
        return Math.sqrt(a * a + b * b);
    }

    public static long inv(long a){
        return quickPOW(a, MOD - 2);
    }

    public class Interval {
        int start;
        int end;
        public Interval(int start, int end) {
            this.start = start;
            this.end = end;
        }
    }

    public static ArrayList<Integer> sieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p]) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        ArrayList<Integer> primeNumbers = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }


    public static int lowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int lowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] >= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static long C(int n, int m)
    {
        if(m == 0 || m == n) return 1l;
        if(m > n || m < 0) return 0l;
        long res = fac[n] * quickPOW((fac[m] * fac[n - m]) % MOD, MOD - 2) % MOD;

        return res;
    }
    public static long quickPOW(long n, long m)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % MOD;
            n = (n * n) % MOD;
            m >>= 1;
        }
        return ans;
    }

    public static int gcd(int a, int b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }
    public static long gcd(long a, long b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }

    static class Randomized {
        public static void shuffle(int[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void shuffle(long[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }
    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper(new Random());

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }

    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}