#include <bits/stdc++.h>
const int sz = 800;
const long long MOD = 1e9 + 9;
long long fib[300050], fibsum[300050], cum[300050], val[300050];
int n, m, x, y, t, p, iter, ql[300050], qr[300050];
int main() {
  fib[0] = fib[1] = 1;
  for (int i = 2; i < 300050; i++) {
    fib[i] = fib[i - 1] + fib[i - 2];
    if (fib[i] > MOD) fib[i] -= MOD;
  }
  fibsum[0] = 1;
  for (int i = 1; i < 300050; i++) {
    fibsum[i] = fib[i] + fibsum[i - 1];
    if (fibsum[i] > MOD) fibsum[i] -= MOD;
  }
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; i++) {
    scanf("%d", &x);
    cum[i + 1] = cum[i] + x;
    if (cum[i + 1] > MOD) cum[i + 1] -= MOD;
  }
  for (int i = 0; i < m; i++) {
    scanf("%d", &t);
    if (iter - p > sz) {
      memset(val, 0, sizeof(val));
      for (int j = p; j < iter; j++) {
        int l = ql[j], r = qr[j];
        val[l] += 1;
        if (val[l] > MOD) val[l] -= MOD;
        val[r + 1] -= fib[r - l + 1];
        if (val[r + 1] < 0) val[r + 1] += MOD;
        val[r + 2] -= fib[r - l];
        if (val[r + 2] < 0) val[r + 2] += MOD;
      }
      p = iter;
      for (int j = 2; j < 300050; j++) {
        val[j] += val[j - 1] + val[j - 2];
        if (val[j] > MOD) val[j] %= MOD;
      }
      long long sum = 0;
      for (int j = 1; j <= n; j++) {
        sum += val[j];
        if (sum > MOD) sum -= MOD;
        cum[j] += sum;
        if (cum[j] > MOD) cum[j] -= MOD;
      }
    }
    if (t == 1) {
      scanf("%d %d", &x, &y);
      ql[iter] = x;
      qr[iter] = y;
      iter++;
    } else {
      scanf("%d %d", &x, &y);
      long long sum = (cum[y] - cum[x - 1] + MOD) % MOD;
      for (int j = p; j < iter; j++) {
        int l = ql[j], r = qr[j];
        if (y < l || r < x)
          continue;
        else if (x <= l && r <= y)
          sum += fibsum[r - l];
        else if (x <= l)
          sum += fibsum[y - l];
        else if (r <= y)
          sum += fibsum[r - l] - fibsum[x - l - 1];
        else
          sum += fibsum[y - l] - fibsum[x - l - 1];
        if (sum > MOD) sum -= MOD;
        if (sum < 0) sum += MOD;
      }
      printf("%I64d\n", sum);
    }
  }
}
