#include <bits/stdc++.h>
using namespace std;
long long f[300005], s[300005], A[300005], tree[1200000];
pair<long long, long long> lazy[1200000];
long long getFib(long long a, long long b, int n) {
  if (n == 1) return a;
  if (n == 2) return b;
  return (a * f[n - 2] + b * f[n - 1]) % 1000000009;
}
long long getSum(long long a, long long b, int n) {
  if (n == 1) return a;
  if (n == 2) return (a + b) % 1000000009;
  return (a * (s[n - 2] + 1) + b * s[n - 1]) % 1000000009;
}
void build(int pos, int l, int r) {
  if (l == r) {
    tree[pos] = A[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(pos * 2, l, mid);
  build(pos * 2 + 1, mid + 1, r);
  tree[pos] = (tree[pos * 2] + tree[pos * 2 + 1]) % 1000000009;
}
void update(int pos, int l, int r, int a, int b) {
  int mid = (l + r) >> 1;
  if (lazy[pos] != make_pair(0LL, 0LL)) {
    tree[pos] =
        (tree[pos] + getSum(lazy[pos].first, lazy[pos].second, r - l + 1)) %
        1000000009;
    if (l != r) {
      lazy[pos * 2].first =
          (lazy[pos * 2].first + lazy[pos].first) % 1000000009;
      lazy[pos * 2].second =
          (lazy[pos * 2].second + lazy[pos].second) % 1000000009;
      lazy[pos * 2 + 1].first =
          (lazy[pos * 2 + 1].first +
           getFib(lazy[pos].first, lazy[pos].second, mid + 1 - l + 1)) %
          1000000009;
      lazy[pos * 2 + 1].second =
          (lazy[pos * 2 + 1].second +
           getFib(lazy[pos].first, lazy[pos].second, mid + 2 - l + 1)) %
          1000000009;
    }
    lazy[pos] = {0, 0};
  }
  if (l > b or r < a) return;
  if (l >= a and r <= b) {
    tree[pos] = (tree[pos] + s[r - a + 1] - s[l - a] + 1000000009) % 1000000009;
    if (l != r) {
      lazy[pos * 2].first = (lazy[pos * 2].first + f[l - a + 1]) % 1000000009;
      lazy[pos * 2].second = (lazy[pos * 2].second + f[l - a + 2]) % 1000000009;
      lazy[pos * 2 + 1].first =
          (lazy[pos * 2 + 1].first + f[mid + 1 - a + 1]) % 1000000009;
      lazy[pos * 2 + 1].second =
          (lazy[pos * 2 + 1].second + f[mid + 2 - a + 1]) % 1000000009;
    }
    return;
  }
  update(pos * 2, l, mid, a, b);
  update(pos * 2 + 1, mid + 1, r, a, b);
  tree[pos] = (tree[pos * 2] + tree[pos * 2 + 1]) % 1000000009;
}
long long query(int pos, int l, int r, int a, int b) {
  int mid = (l + r) >> 1;
  if (lazy[pos] != make_pair(0LL, 0LL)) {
    tree[pos] =
        (tree[pos] + getSum(lazy[pos].first, lazy[pos].second, r - l + 1)) %
        1000000009;
    if (l != r) {
      lazy[pos * 2].first =
          (lazy[pos * 2].first + lazy[pos].first) % 1000000009;
      lazy[pos * 2].second =
          (lazy[pos * 2].second + lazy[pos].second) % 1000000009;
      lazy[pos * 2 + 1].first =
          (lazy[pos * 2 + 1].first +
           getFib(lazy[pos].first, lazy[pos].second, mid + 1 - l + 1)) %
          1000000009;
      lazy[pos * 2 + 1].second =
          (lazy[pos * 2 + 1].second +
           getFib(lazy[pos].first, lazy[pos].second, mid + 2 - l + 1)) %
          1000000009;
    }
    lazy[pos] = {0, 0};
  }
  if (l > b or r < a) return 0;
  if (l >= a and r <= b) return tree[pos];
  return (query(pos * 2, l, mid, a, b) + query(pos * 2 + 1, mid + 1, r, a, b)) %
         1000000009;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, m, i, t, l, r;
  f[1] = f[2] = 1;
  for (i = 3; i <= 300000; i++) f[i] = (f[i - 1] + f[i - 2]) % 1000000009;
  for (i = 1; i <= 300000; i++) s[i] = (s[i - 1] + f[i]) % 1000000009;
  cin >> n >> m;
  for (i = 1; i <= n; i++) cin >> A[i];
  build(1, 1, n);
  while (m--) {
    cin >> t >> l >> r;
    if (t == 1)
      update(1, 1, n, l, r);
    else
      cout << query(1, 1, n, l, r) << '\n';
  }
  return 0;
}
