In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation 

F1 = 1; F2 = 1; Fn = Fn - 1 + Fn - 2 (n > 2).

DZY loves Fibonacci numbers very much. Today DZY gives you an array consisting of n integers: a1, a2, ..., an. Moreover, there are m queries, each query has one of the two types:

  1. Format of the query "1 l r". In reply to the query, you need to add Fi - l + 1 to each element ai, where l ≤ i ≤ r. 
  2. Format of the query "2 l r". In reply to the query you should output the value of <image> modulo 1000000009 (109 + 9). 



Help DZY reply to all the queries.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 300000). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — initial array a.

Then, m lines follow. A single line describes a single query in the format given in the statement. It is guaranteed that for each query inequality 1 ≤ l ≤ r ≤ n holds.

Output

For each query of the second type, print the value of the sum on a single line.

Examples

Input

4 4
1 2 3 4
1 1 4
2 1 4
1 2 4
2 1 3


Output

17
12

Note

After the first query, a = [2, 3, 5, 7].

For the second query, sum = 2 + 3 + 5 + 7 = 17.

After the third query, a = [2, 4, 6, 9].

For the fourth query, sum = 2 + 4 + 6 = 12.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        private static final int MOD = 1000000009;
        int[] A;
        int[] Aint;
        int[] A1;
        int[] A2;
        int a;
        int b;
        int[][][] fib;
        int[][][] sumFib;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            int M = in.nextInt();
            A = new int[N];
            for (int i = 0; i < N; i++) {
                A[i] = in.nextInt();
            }
            Aint = new int[4 * N];
            A1 = new int[4 * N];
            A2 = new int[4 * N];
            init(1, 0, N - 1);
            int[][] mat = new int[][]{
                    { 0, 1 },
                    { 1, 1 }
            };
            fib = new int[N][2][2];
            sumFib = new int[N][2][2];
            fib[0] = new int[][]{
                    { 1, 0 },
                    { 0, 1 }
            };
            sumFib[0] = fib[0];
            for (int p = 1; p < N; p++) {
                for (int i = 0; i < 2; i++) {
                    for (int j = 0; j < 2; j++) {
                        for (int k = 0; k < 2; k++) {
                            fib[p][i][j] = (int) ((fib[p][i][j] + (long)fib[p - 1][i][k] * mat[k][j]) % MOD);
                        }
                    }
                }
                for (int i = 0; i < 2; i++) {
                    for (int j = 0; j < 2; j++) {
                        sumFib[p][i][j] = sumFib[p - 1][i][j] + fib[p][i][j];
                        if (sumFib[p][i][j] >= MOD) {
                            sumFib[p][i][j] -= MOD;
                        }
                    }
                }
            }
            for (int i = 0; i < M; i++) {
                int t = in.nextInt();
                a = in.nextInt() - 1;
                b = in.nextInt() - 1;
                if (t == 1) {
                    update(1, 0, N - 1);
                }
                else {
                    int q = query(1, 0, N - 1);
                    out.println(q);
                }
            }
        }
        private int query(int k, int st, int dr) {
            if (a <= st && dr <= b) {
                return Aint[k];
            }
            push(k, st, dr);
            int m = (st + dr) / 2;
            int ret = 0;
            if (a <= m) {
                ret += query(2 * k, st, m);
                if (ret >= MOD) {
                    ret -= MOD;
                }
            }
            if (b > m) {
                ret += query(2 * k + 1, m + 1, dr);
                if (ret >= MOD) {
                    ret -= MOD;
                }
            }
            return ret;
        }
        private void update(int k, int st, int dr) {
            if (a <= st && dr <= b) {
                Aint[k] += getSum(1, 1, st - a, dr - a);
                if (Aint[k] >= MOD) {
                    Aint[k] -= MOD;
                }
                A1[k] += getElem(1, 1, st - a);
                if (A1[k] >= MOD) {
                    A1[k] -= MOD;
                }
                if (st < dr) {
                    A2[k] += getElem(1, 1, st - a + 1);
                    if (A2[k] >= MOD) {
                        A2[k] -= MOD;
                    }
                }
                return;
            }
            push(k, st, dr);
            int m = (st + dr) / 2;
            if (a <= m) {
                update(2 * k, st, m);
            }
            if (m < b) {
                update(2 * k + 1, m + 1, dr);
            }
            Aint[k] = Aint[2 * k] + Aint[2 * k + 1];
            if (Aint[k] >= MOD) {
                Aint[k] -= MOD;
            }
        }
        private void push(int k, int st, int dr) {
            int m = (st + dr) / 2;

            A1[2 * k] += A1[k];
            if (A1[2 * k] >= MOD) {
                A1[2 * k] -= MOD;
            }
            A2[2 * k] += A2[k];
            if (A2[2 * k] >= MOD) {
                A2[2 * k] -= MOD;
            }
            A1[2 * k + 1] += getElem(A1[k], A2[k], m + 1 - st);
            if (A1[2 * k + 1] >= MOD) {
                A1[2 * k + 1] -= MOD;
            }
            A2[2 * k + 1] += getElem(A1[k], A2[k], m + 1 - st + 1);
            if (A2[2 * k + 1] >= MOD) {
                A2[2 * k + 1] -= MOD;
            }

            Aint[2 * k] += getSum(A1[k], A2[k], 0, m - st);
            if (Aint[2 * k] >= MOD) {
                Aint[2 * k] -= MOD;
            }
            Aint[2 * k + 1] += getSum(A1[k], A2[k], m + 1 - st, dr - st);
            if (Aint[2 * k + 1] >= MOD) {
                Aint[2 * k + 1] -= MOD;
            }
            A1[k] = A2[k] = 0;
        }
        private int getElem(int a, int b, int k) {
            return (int) (((long) fib[k][0][0] * a + (long) fib[k][0][1] * b) % MOD);
        }
        private int getSum(int a, int b, int st, int dr) {
            int ret = getSingleSum(a, b, dr);
            if (st > 0) {
                ret -= getSingleSum(a, b, st - 1);
                if (ret < 0) {
                    ret += MOD;
                }
            }
            return ret;
        }
        private int getSingleSum(int a, int b, int k) {
            return (int) (((long) sumFib[k][0][0] * a + (long) sumFib[k][0][1] * b) % MOD);
        }
        private void init(int k, int st, int dr) {
            if (st == dr) {
                Aint[k] = A[st];
                return;
            }
            int m = (st + dr) / 2;
            init(2 * k, st, m);
            init(2 * k + 1, m + 1, dr);
            Aint[k] = Aint[2 * k] + Aint[2 * k + 1];
            if (Aint[k] >= MOD) {
                Aint[k] -= MOD;
            }
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt(){
            return Integer.parseInt(next());
        }
        public long nextLong() { return Long.parseLong(next()); }
    }
}