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;
using LL = long long;
const int MAXN = 300010;
LL D[MAXN << 2];
LL sumTree[MAXN << 2], arr[MAXN], maxArr[MAXN << 2];
void pushup(unsigned rootIndex) {
  sumTree[rootIndex] = sumTree[rootIndex << 1] + sumTree[rootIndex << 1 | 1];
  maxArr[rootIndex] = max(maxArr[rootIndex << 1], maxArr[rootIndex << 1 | 1]);
}
void build(unsigned tl, unsigned tr, unsigned rootIndex) {
  if (tl == tr) {
    sumTree[rootIndex] = maxArr[rootIndex] = arr[tl];
    return;
  }
  unsigned midIndex = (tl + tr) >> 1;
  build(tl, midIndex, rootIndex << 1);
  build(midIndex + 1, tr, rootIndex << 1 | 1);
  pushup(rootIndex);
}
void update(unsigned QL, unsigned QR, unsigned tl, unsigned tr,
            unsigned rootIndex) {
  if (maxArr[rootIndex] <= 2) {
    return;
  } else if (tl == tr) {
    sumTree[rootIndex] = maxArr[rootIndex] = D[sumTree[rootIndex]];
    return;
  }
  unsigned midIndex = (tl + tr) >> 1;
  if (QL <= midIndex) {
    update(QL, QR, tl, midIndex, rootIndex << 1);
  }
  if (midIndex < QR) {
    update(QL, QR, midIndex + 1, tr, rootIndex << 1 | 1);
  }
  pushup(rootIndex);
}
LL query(unsigned QL, unsigned QR, unsigned tl, unsigned tr,
         unsigned rootIndex) {
  if (QL <= tl && tr <= QR) {
    return sumTree[rootIndex];
  }
  unsigned midIndex = (tl + tr) >> 1;
  LL ans = 0;
  if (QL <= midIndex) {
    ans += query(QL, QR, tl, midIndex, rootIndex << 1);
  }
  if (QR > midIndex) {
    ans += query(QL, QR, midIndex + 1, tr, rootIndex << 1 | 1);
  }
  return ans;
}
int main() {
  int n, midIndex, i, j;
  for (i = 1; i <= 1000000; i++) {
    for (j = i; j <= 1000000; j += i) {
      D[j]++;
    }
  }
  scanf("%d%d", &n, &midIndex);
  for (i = 1; i <= n; i++) scanf("%lld", &arr[i]);
  build(1, n, 1);
  int t, a, b;
  for (i = 0; i < midIndex; i++) {
    scanf("%d%d%d", &t, &a, &b);
    if (t == 1) {
      update(a, b, 1, n, 1);
    } else {
      printf("%lld\n", query(a, b, 1, n, 1));
    }
  }
  return 0;
}