#include <bits/stdc++.h>
using namespace std;
int a[300005];
int asum[300005];
vector<pair<int, int> > recent;
int F[300005];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
    asum[i + 1] = (asum[i] + a[i]) % 1000000009;
  }
  F[1] = 1;
  F[2] = 1;
  for (int i = 3; i < 300005; ++i) F[i] = (F[i - 1] + F[i - 2]) % 1000000009;
  for (int i = 0; i < m; ++i) {
    int type, l, r;
    scanf("%d%d%d", &type, &l, &r);
    --r;
    --l;
    if (type == 1) {
      recent.push_back(make_pair(l, r));
      if (recent.size() > 1033) {
        for (int j = 0; j < n; ++j) a[j] = 0;
        for (int j = 0; j < recent.size(); ++j) {
          a[recent[j].first]++;
          a[recent[j].second + 1] =
              (a[recent[j].second + 1] + 1000000009 -
               F[recent[j].second - recent[j].first + 2]) %
              1000000009;
          a[recent[j].second + 2] =
              (a[recent[j].second + 2] + 1000000009 -
               F[recent[j].second - recent[j].first + 1]) %
              1000000009;
        }
        for (int j = 1; j < n; ++j) {
          if (j > 1) a[j] = (a[j] + a[j - 2]) % 1000000009;
          a[j] = (a[j] + a[j - 1]) % 1000000009;
        }
        int s = 0;
        for (int j = 0; j < n; ++j) {
          s = (s + a[j]) % 1000000009;
          asum[j + 1] = (asum[j + 1] + s) % 1000000009;
        }
        recent.clear();
      }
    } else {
      int ans = asum[r + 1] - asum[l];
      ans = (ans + 1000000009) % 1000000009;
      for (int j = 0; j < recent.size(); ++j) {
        int add;
        int start, stop;
        if (l > recent[j].first)
          start = l;
        else
          start = recent[j].first;
        if (r > recent[j].second)
          stop = recent[j].second;
        else
          stop = r;
        if (stop < start - 1) continue;
        start -= recent[j].first;
        stop -= recent[j].first;
        add = F[stop + 3] - F[start + 2] + 1000000009;
        add %= 1000000009;
        ans = (ans + add) % 1000000009;
      }
      ans = (ans + 1000000009) % 1000000009;
      printf("%d\n", ans);
    }
  }
  return 0;
}
