#include <bits/stdc++.h>
using namespace std;
const int N = 3e5 + 2, M = 5e3, md = 1e9 + 9;
int n, m, a[N], sz, s[N], pre_fib[N], p[N], pp[N], f[N];
int type[M], l[M], r[M];
char wr[11];
void solve() {
  for (int i = 0; i < sz; ++i)
    if (type[i] == 2) {
      int L = l[i], R = r[i];
      int sum = (0LL + s[R] - s[L - 1] + md) % md;
      for (int j = 0; j < i; ++j)
        if (type[j] == 1) {
          int RR = min(R, r[j]), LL = max(L, l[j]);
          if (LL > RR) continue;
          sum = (sum + 0LL +
                 (0LL + pre_fib[RR - l[j] + 1] - pre_fib[LL - l[j]] + md)) %
                md;
        }
      printf("%d\n", sum);
    }
}
void rebuild() {
  for (int i = 0; i < sz; ++i)
    if (type[i] == 1) {
      p[l[i]] = (p[l[i]] + 1) % md;
      p[r[i] + 1] = (0LL + p[r[i] + 1] - f[r[i] - l[i] + 2] + md) % md,
               pp[r[i] + 1] =
                   (0LL + pp[r[i] + 1] - f[r[i] - l[i] + 1] + md) % md;
    }
  int P = 0, PP = 0;
  for (int i = 1; i <= n; ++i) {
    P = (P + p[i]) % md;
    PP = (PP + pp[i]) % md;
    p[i] = pp[i] = 0;
    a[i] = (a[i] + P) % md;
    s[i] = (s[i - 1] + a[i]) % md;
    swap(P, PP);
    P = (P + PP) % md;
  }
}
void read(int &first) {
  first = 0;
  while (1) {
    char ch = getchar();
    if (ch == ' ' || ch == '\n') break;
    first = first * 10 + ch - '0';
  }
}
int main() {
  read(n);
  read(m);
  for (int i = 1; i <= n; ++i) read(a[i]), s[i] = (s[i - 1] + a[i]) % md;
  f[1] = f[2] = 1;
  for (int i = 3; i < N; ++i) f[i] = (f[i - 1] + f[i - 2]) % md;
  for (int i = 1; i < N; ++i) pre_fib[i] = (pre_fib[i - 1] + f[i]) % md;
  int LN = 2.7 * sqrt(m);
  while (m--) {
    read(type[sz]);
    read(l[sz]);
    read(r[sz]);
    ++sz;
    if (sz == LN) {
      solve();
      rebuild();
      sz = 0;
    }
  }
  solve();
}
