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;
long long a[3000000], sum[3000000 << 2], add[3000000 << 2];
void pushup(int rt) {
  sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
  add[rt] = max(add[rt << 1], add[rt << 1 | 1]);
}
long long d[3000000];
void init() {
  for (int i = 1; i < 3000000; i++) {
    for (int j = i; j < 3000000; j += i) {
      d[j]++;
    }
  }
}
void build(int l, int r, int rt) {
  if (l == r) {
    sum[rt] = add[rt] = a[l];
    return;
  }
  int m = (l + r) >> 1;
  build(l, m, rt << 1);
  build(m + 1, r, rt << 1 | 1);
  pushup(rt);
}
void updateM(int L, int R, int l, int r, int rt) {
  if (add[rt] <= 2) return;
  if (l == r) {
    sum[rt] = add[rt] = d[sum[rt]];
    return;
  }
  int m = (l + r) >> 1;
  if (L <= m) updateM(L, R, l, m, rt << 1);
  if (R > m) updateM(L, R, m + 1, r, rt << 1 | 1);
  pushup(rt);
}
long long query(int L, int R, int l, int r, int rt) {
  if (L <= l && R >= r) {
    return sum[rt];
  }
  int m = (l + r) >> 1;
  long long ans = 0;
  if (L <= m) ans += query(L, R, l, m, rt << 1);
  if (R > m) ans += query(L, R, m + 1, r, rt << 1 | 1);
  return ans;
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  init();
  build(1, n, 1);
  while (m--) {
    int a, b, c;
    scanf("%d%d%d", &a, &b, &c);
    if (a == 1)
      updateM(b, c, 1, n, 1);
    else
      cout << query(b, c, 1, n, 1) << endl;
  }
  return 0;
}