#include <bits/stdc++.h>
using namespace std;
const int N = 300000 + 1;
const int inf = (int)1e9 + 1;
const long long big = (long long)1e18 + 1;
const int P = 239;
const int MOD = (int)1e9 + 9;
const int MOD1 = (int)1e9 + 9;
const double eps = 1e-9;
const double pi = atan2(0, -1);
const int ABC = 26;
const int B = 555;
long long fib[400000];
void init() {
  fib[1] = 1;
  fib[2] = 1;
  for (int i = 2; i < 400000; i++) {
    fib[i] = fib[i - 1] + fib[i - 2];
    if (fib[i] >= MOD) fib[i] -= MOD;
  }
}
int n;
long long a[N], pref[N], add[N];
vector<pair<int, int> > temp;
void update() {
  fill(add, add + n, 0);
  for (auto it : temp) {
    int l = it.first, r = it.second;
    add[l]++;
    if (add[l] >= MOD) add[l] -= MOD;
    if (r + 1 < n) {
      add[r + 1] -= fib[(r - l + 1) + 1];
      if (add[r + 1] < 0) add[r + 1] += MOD;
    }
    if (r + 2 < n) {
      add[r + 2] -= fib[(r - l + 1)];
      if (add[r + 2] < 0) add[r + 2] += MOD;
    }
  }
  temp.clear();
  for (int i = 1; i < n; i++) {
    add[i] += add[i - 1];
    if (add[i] >= MOD) add[i] -= MOD;
    if (i > 1) {
      add[i] += add[i - 2];
      if (add[i] >= MOD) add[i] -= MOD;
    }
  }
  for (int i = 0; i < n; i++) {
    a[i] += add[i];
    if (a[i] >= MOD) a[i] -= MOD;
  }
  pref[0] = 0;
  for (int i = 0; i < n; i++) {
    pref[i + 1] = pref[i] + a[i];
    if (pref[i + 1] >= MOD) pref[i + 1] -= MOD;
  }
}
long long fib_sum(int x) {
  long long res = fib[x + 2] - 1;
  if (res < 0) res += MOD;
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.precision(20);
  init();
  int m;
  cin >> n >> m;
  for (int i = 0; i < n; i++) cin >> a[i];
  update();
  for (int i = 0; i < m; i++) {
    int t, l, r;
    cin >> t >> l >> r;
    l--;
    r--;
    if (t == 1) {
      temp.push_back({l, r});
      if ((int)temp.size() > B) update();
    } else {
      long long ans = pref[r + 1] - pref[l];
      if (ans < 0) ans += MOD;
      for (auto it : temp)
        if (max(l, it.first) <= min(r, it.second)) {
          ans += fib_sum(min(r, it.second) - it.first + 1);
          if (ans >= MOD) ans -= MOD;
          ans -= fib_sum(max(l, it.first) - it.first);
          if (ans < 0) ans += MOD;
        }
      cout << ans << "\n";
    }
  }
  return 0;
}
