Problem: Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).

You are given an array a of n integers. You have to process two types of queries:

  1. REPLACE l r — for every <image> replace ai with D(ai); 
  2. SUM l r — calculate <image>. 



Print the answer for each SUM query.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 3·105) — the number of elements in the array and the number of queries to process, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the elements of the array.

Then m lines follow, each containing 3 integers ti, li, ri denoting i-th query. If ti = 1, then i-th query is REPLACE li ri, otherwise it's SUM li ri (1 ≤ ti ≤ 2, 1 ≤ li ≤ ri ≤ n).

There is at least one SUM query.

Output

For each SUM query print the answer to it.

Example

Input

7 6
6 4 1 10 3 2 4
2 1 7
2 4 5
1 3 5
2 4 4
1 5 7
2 1 7


Output

30
13
4
22

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int inf = 0x7fffffff;
const int N = 1e6 + 100;
const int M = 3 * 1e5 + 100;
long long tree[M << 2], d[N], mx[M << 2];
int n, m;
void init() {
  for (int i = 1; i < N; i++)
    for (int j = i; j < N; j += i) d[j]++;
}
void push_up(int rt) {
  tree[rt] = tree[rt << 1] + tree[rt << 1 | 1];
  mx[rt] = max(mx[rt << 1], mx[rt << 1 | 1]);
}
void build(int rt, int l, int r) {
  if (l == r) {
    scanf("%lld", &tree[rt]);
    mx[rt] = tree[rt];
    return;
  }
  int m = (l + r) / 2;
  build(rt << 1, l, m);
  build(rt << 1 | 1, m + 1, r);
  push_up(rt);
}
void update(int L, int R, int rt, int l, int r) {
  if (mx[rt] <= 2) return;
  if (l == r) {
    tree[rt] = mx[rt] = d[tree[rt]];
    return;
  }
  int m = (l + r) / 2;
  if (L <= m) update(L, R, rt << 1, l, m);
  if (R > m) update(L, R, rt << 1 | 1, m + 1, r);
  push_up(rt);
}
long long query(int L, int R, int rt, int l, int r) {
  if (L <= l && r <= R) return tree[rt];
  long long ans = 0;
  int m = (l + r) / 2;
  if (L <= m) ans += query(L, R, rt << 1, l, m);
  if (R > m) ans += query(L, R, rt << 1 | 1, m + 1, r);
  return ans;
}
int main() {
  init();
  scanf("%d %d", &n, &m);
  build(1, 1, n);
  while (m--) {
    int k, l, r;
    scanf("%d %d %d", &k, &l, &r);
    if (k == 1)
      update(l, r, 1, 1, n);
    else
      cout << query(l, r, 1, 1, n) << endl;
  }
  return 0;
}