#include <bits/stdc++.h>
using namespace std;
// #define FOR(i, begin, end) for (__typeof(end) i = (begin); i != (end) + 1 - 2 * ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))

#define _upgrade ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define FOR(i, a, b) for (int i = a; i <= b; i++)
#define FORB(i, a, b) for (int i = a; i >= b; i--)
#define REP(i, a) for (int i = 0; i < a; i++)
#define REP1(i, a) for (int i = 1; i < a; i++)
#define REPB(i, a) for (int i = a - 1; i >= 0; i--)
#define TRAV(a,x) for (auto& a: x)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define II <int, int>
#define Q queue
#define ff first
#define bk back()
#define ss second
#define rs resize
#define ins insert 
#define fr front() 
#define ts to_string
#define pb push_back
#define mp make_pair
#define lb lower_bound 
#define ub upper_bound 
#define PQ priority_queue
#define umap unordered_map
#define sz(x) (int)x.size()

typedef long long ll;
typedef double db;
typedef unsigned uint;
typedef unsigned long long ull;
typedef unordered_map<int, int> umapII;
// PQ going up <int, VI, greater<int> >
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<bool> VB;
typedef vector<VB> VVB;
typedef vector<VVB> VVVB;
typedef vector<umapII> VumapII;
typedef vector<ll> VLL;
typedef vector<VLL> VVLL;
typedef vector<VVLL> VVVLL;
typedef vector<VVVLL> VVVVLL;
typedef vector<db> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<PII> VPI;
typedef vector<VPI> VVPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VVVI> VVVVI;
typedef vector<VVVVI> VVVVVI;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
 
void eraseDups(VI& a) {
    a.erase(unique(a.begin(), a.end()), a.end());
}
int strToInt(string&a) {
    stringstream x(a);
    int b;
    x >> b;
    return b;
}
void readI(int& a) {
    cin >> a;
}
void readI(int& a, int&b) {
    cin >> a >> b;
}
void readI(int& a, int&b, int&c) {
    cin >> a >> b >> c;
}
VI readVI(int n) {
    VI a(n);
    REP(i, n) cin >> a[i];
    return a;
}
VVI readVVI(int n, int m) {
    VVI a(n, VI(m));
    REP(i, n) a[i] = readVI(m);
    return a;
}
VLL readVLL(ll n) {
    VLL a(n);
    REP(i, n) cin >> a[i];
    return a;
}
VVLL readVVLL(ll n, ll m) {
    VVLL a(n, VLL(m));
    REP(i, n) a[i] = readVLL(m);
    return a;
}


int gcd(int a, int b) {
   if (b == 0) return a;
   return gcd(b, a % b);
}

void print(VI& a) {
    for (auto el : a) {
        cout << el << ' ';
    }
    cout << '\n';
}

void print(VI& a, int n) {
    int cnt = 0;
    for (auto el : a) {
        if (cnt++ == n) break;
        cout << el << ' ';
    }
    cout << '\n';
}
const int MOD = 1e9 + 7;
const int INF = 2e9;
const ll INFF = INT64_MAX;
const db EPS = 1e-9;
const db PI = acos(-1.0); //M_PI;
const int moveX[] = {-1, 0, 1, 0};
const int moveY[] = {0, 1, 0, -1};
/*
|      ⣠⣶⡾⠏⠉⠙⠳⢦⡀⠀  ⠀⢠⠞⠉⠙⠲⡀
|  ⠀⠀⣴⠿⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀  ⡏⠀⠀ ⠀⠀ ⢷
|⠀⠀⢠⣟⣋⡀⢀⣀⣀⡀⠀⣀⡀⣧⠀  ⢸⠀⠀⠀⠀   ⡇ ⠀
| ⠀⢸⣯⡭⠁⠸⣛⣟⠆⡴⣻⡲⣿   ⣸⠀⠀OK.  ⡇
|⠀⠀⣟⣿⡭⠀⠀⠀⠀⠀⢱⠀⠀⣿   ⢹⠀⠀⠀⠀⠀ ⡇
|⠀⠀⠙⢿⣯⠄⠀⠀⠀⢀⡀⠀⠀⡿⠀  ⡇⠀⠀ ⠀ ⡼
|⠀⠀⠀⠀⠹⣶⠆⠀⠀⠀⠀⠀⡴⠃ ⠀ ⠘⠤⣄⣠⠞⠀ ⠀
|⠀⠀⠀⠀⢸⣷⡦⢤⡤⢤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
|⠀⢀⣤⣴⣿⣏⠁⠀⠀⠸⣏⢯⣷⣖⣦⡀⠀⠀⠀⠀⠀⠀
|⢀⣾⣽⣿⣿⣿⣿⠛⢲⣶⣾⢉⡷⣿⣿⠵⣿⠀⠀⠀⠀⠀
|⣼⣿⠍⠉⣿⡭⠉⠙⢺⣇⣼⡏⠀ ⠀⣄⢸⣿
|⣿⣿⣧⣀⣿.........⣀⣰⣏⣘⣆⣀
      
|                                                   _         _   _
|                                                   (_)       | | | |
|_ __  _ __ ___   __ _ _ __ __ _ _ __ ___  _ __ ___  _ ___ ___| |_| |_
| '_ \| '__/ _ \ / _` | '__/ _` | '_ ` _ \| '_ ` _ \| / __/ __| __| __|
| |_) | | | (_) | (_| | | | (_| | | | | | | | | | | | \__ \__ \ |_| |_
| .__/|_|  \___/ \__, |_|  \__,_|_| |_| |_|_| |_| |_|_|___/___/\__|\__|
| |               __/ |
|_|              |___/
 _   _      _ _    __        __         _     _ 
| | | | ___| | | __\ \      / /__  _ __| | __| |
| |_| |/ _ \ | |/ _ \ \ /\ / / _ \| '__| |/ _` |
|  _  |  __/ | | (_) \ V  V / (_) | |  | | (_| |
|_| |_|\___|_|_|\___/ \_/\_/ \___/|_|  |_|\__,_|                                  
 ____     __    _______    _______   __________
|     \  |  |  |  _____|  /  _____) |____  ____|
|  |\  \ |  |  | |__     (  (_____      |  |
|  | \  \|  |  |  __|     \_____  \     |  | 
|  |  \     |  | |_____    _____)  )    |  | 
|__|   \____|  |_______|  (_______/     |__| 
 
 
 


*/









vector<int> smallest_factor;
vector<bool> prime;
vector<int> primes;

void sieve(int maximum) {
    maximum = max(maximum, 1);
    smallest_factor.assign(maximum + 1, 0);
    prime.assign(maximum + 1, true);
    prime[0] = prime[1] = false;
    primes.clear();
    for (int p = 2; p <= maximum; p++)
        if (prime[p]) {
            smallest_factor[p] = p;
            primes.push_back(p);
            for (long long i = (long long)p * p; i <= maximum; i += p)
                if (prime[i]) {
                    prime[i] = false;
                    smallest_factor[i] = p;
                }
        }
}

const int N = 1e5 + 5;
VI nex(N), seen(N, N);
VVI dp(N+5, VI(20, N));
int n;
void go () {
    int n, m;
    cin >> n >> m; 
    VI nums = readVI(n);
    nex[n] = n;
    for (int i = n - 1; i >= 0; i--) {
        nex[i] = nex[i+1];
        int tmp = nums[i];
        for (auto el : primes) {
            bool x = 0;
            while(tmp % el == 0) {
                x = 1;
                tmp /= el;
            }
            if (x) {
                nex[i] = min(nex[i], seen[el]);
                seen[el] = i;
            }
        }
        if (tmp != 1) {
            nex[i] = min(nex[i], seen[tmp]);
            seen[tmp] = i;
        }
    }
    //dp[i][j] i-r 2^j
    // print(nex, n+5);
    REP(i, n) 
        dp[i][0] = nex[i];
        
    REP1(j, 20) 
    REP(i, n) 
        dp[i][j] = dp[dp[i][j-1]][j-1]; 
    
    while(m--) {
        int l, r;
        cin >> l >> r;
        l--, r--;
        int st = l, cnt = 0;
        // while(st < r) {
        // cout << st << ' ';
        for (int i = 19; i >= 0; i--) {
            if (dp[st][i] <= r) {
                st = dp[st][i];
                // cout << i << ',' << st << ' ';
                cnt += (1<<i);
            }
        }
        // }
        // cout << "\n";
        cout << cnt+1 << '\n';
    }
    // print(nex, n);
}

void init() {
    int limit = sqrt(1e5)+5;
    sieve(limit);
    // m = primes.size();
    // cout << primes.size() << '\n';
}


signed main () {

#ifdef ONLINE_JUDGE
#else
    freopen("in.txt", "r", stdin);
//	freopen("out.txt", "w", stdout);
#endif
    _upgrade
    int T = 1;
    init();
    while(T--) go();
    return 0;
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
    
*/
### Prompt

Please formulate a CPP solution to the following problem:

This time Baby Ehab will only cut and not stick. He starts with a piece of paper with an array a of length n written on it, and then he does the following:

  * he picks a range (l, r) and cuts the subsegment a_l, a_{l + 1}, …, a_r out, removing the rest of the array. 
  * he then cuts this range into multiple subranges. 
  * to add a number theory spice to it, he requires that the elements of every subrange must have their product equal to their [least common multiple (LCM)](https://en.wikipedia.org/wiki/Least_common_multiple). 



Formally, he partitions the elements of a_l, a_{l + 1}, …, a_r into contiguous subarrays such that the product of every subarray is equal to its LCM. Now, for q independent ranges (l, r), tell Baby Ehab the minimum number of subarrays he needs.

Input

The first line contains 2 integers n and q (1 ≤ n,q ≤ 10^5) — the length of the array a and the number of queries.

The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^5) — the elements of the array a.

Each of the next q lines contains 2 integers l and r (1 ≤ l ≤ r ≤ n) — the endpoints of this query's interval.

Output

For each query, print its answer on a new line.

Example

Input


6 3
2 3 10 7 5 14
1 6
2 4
3 5


Output


3
1
2

Note

The first query asks about the whole array. You can partition it into [2], [3,10,7], and [5,14]. The first subrange has product and LCM equal to 2. The second has product and LCM equal to 210. And the third has product and LCM equal to 70. Another possible partitioning is [2,3], [10,7], and [5,14].

The second query asks about the range (2,4). Its product is equal to its LCM, so you don't need to partition it further.

The last query asks about the range (3,5). You can partition it into [10,7] and [5].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
// #define FOR(i, begin, end) for (__typeof(end) i = (begin); i != (end) + 1 - 2 * ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))

#define _upgrade ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define FOR(i, a, b) for (int i = a; i <= b; i++)
#define FORB(i, a, b) for (int i = a; i >= b; i--)
#define REP(i, a) for (int i = 0; i < a; i++)
#define REP1(i, a) for (int i = 1; i < a; i++)
#define REPB(i, a) for (int i = a - 1; i >= 0; i--)
#define TRAV(a,x) for (auto& a: x)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define II <int, int>
#define Q queue
#define ff first
#define bk back()
#define ss second
#define rs resize
#define ins insert 
#define fr front() 
#define ts to_string
#define pb push_back
#define mp make_pair
#define lb lower_bound 
#define ub upper_bound 
#define PQ priority_queue
#define umap unordered_map
#define sz(x) (int)x.size()

typedef long long ll;
typedef double db;
typedef unsigned uint;
typedef unsigned long long ull;
typedef unordered_map<int, int> umapII;
// PQ going up <int, VI, greater<int> >
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<bool> VB;
typedef vector<VB> VVB;
typedef vector<VVB> VVVB;
typedef vector<umapII> VumapII;
typedef vector<ll> VLL;
typedef vector<VLL> VVLL;
typedef vector<VVLL> VVVLL;
typedef vector<VVVLL> VVVVLL;
typedef vector<db> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<PII> VPI;
typedef vector<VPI> VVPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VVVI> VVVVI;
typedef vector<VVVVI> VVVVVI;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
 
void eraseDups(VI& a) {
    a.erase(unique(a.begin(), a.end()), a.end());
}
int strToInt(string&a) {
    stringstream x(a);
    int b;
    x >> b;
    return b;
}
void readI(int& a) {
    cin >> a;
}
void readI(int& a, int&b) {
    cin >> a >> b;
}
void readI(int& a, int&b, int&c) {
    cin >> a >> b >> c;
}
VI readVI(int n) {
    VI a(n);
    REP(i, n) cin >> a[i];
    return a;
}
VVI readVVI(int n, int m) {
    VVI a(n, VI(m));
    REP(i, n) a[i] = readVI(m);
    return a;
}
VLL readVLL(ll n) {
    VLL a(n);
    REP(i, n) cin >> a[i];
    return a;
}
VVLL readVVLL(ll n, ll m) {
    VVLL a(n, VLL(m));
    REP(i, n) a[i] = readVLL(m);
    return a;
}


int gcd(int a, int b) {
   if (b == 0) return a;
   return gcd(b, a % b);
}

void print(VI& a) {
    for (auto el : a) {
        cout << el << ' ';
    }
    cout << '\n';
}

void print(VI& a, int n) {
    int cnt = 0;
    for (auto el : a) {
        if (cnt++ == n) break;
        cout << el << ' ';
    }
    cout << '\n';
}
const int MOD = 1e9 + 7;
const int INF = 2e9;
const ll INFF = INT64_MAX;
const db EPS = 1e-9;
const db PI = acos(-1.0); //M_PI;
const int moveX[] = {-1, 0, 1, 0};
const int moveY[] = {0, 1, 0, -1};
/*
|      ⣠⣶⡾⠏⠉⠙⠳⢦⡀⠀  ⠀⢠⠞⠉⠙⠲⡀
|  ⠀⠀⣴⠿⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀  ⡏⠀⠀ ⠀⠀ ⢷
|⠀⠀⢠⣟⣋⡀⢀⣀⣀⡀⠀⣀⡀⣧⠀  ⢸⠀⠀⠀⠀   ⡇ ⠀
| ⠀⢸⣯⡭⠁⠸⣛⣟⠆⡴⣻⡲⣿   ⣸⠀⠀OK.  ⡇
|⠀⠀⣟⣿⡭⠀⠀⠀⠀⠀⢱⠀⠀⣿   ⢹⠀⠀⠀⠀⠀ ⡇
|⠀⠀⠙⢿⣯⠄⠀⠀⠀⢀⡀⠀⠀⡿⠀  ⡇⠀⠀ ⠀ ⡼
|⠀⠀⠀⠀⠹⣶⠆⠀⠀⠀⠀⠀⡴⠃ ⠀ ⠘⠤⣄⣠⠞⠀ ⠀
|⠀⠀⠀⠀⢸⣷⡦⢤⡤⢤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
|⠀⢀⣤⣴⣿⣏⠁⠀⠀⠸⣏⢯⣷⣖⣦⡀⠀⠀⠀⠀⠀⠀
|⢀⣾⣽⣿⣿⣿⣿⠛⢲⣶⣾⢉⡷⣿⣿⠵⣿⠀⠀⠀⠀⠀
|⣼⣿⠍⠉⣿⡭⠉⠙⢺⣇⣼⡏⠀ ⠀⣄⢸⣿
|⣿⣿⣧⣀⣿.........⣀⣰⣏⣘⣆⣀
      
|                                                   _         _   _
|                                                   (_)       | | | |
|_ __  _ __ ___   __ _ _ __ __ _ _ __ ___  _ __ ___  _ ___ ___| |_| |_
| '_ \| '__/ _ \ / _` | '__/ _` | '_ ` _ \| '_ ` _ \| / __/ __| __| __|
| |_) | | | (_) | (_| | | | (_| | | | | | | | | | | | \__ \__ \ |_| |_
| .__/|_|  \___/ \__, |_|  \__,_|_| |_| |_|_| |_| |_|_|___/___/\__|\__|
| |               __/ |
|_|              |___/
 _   _      _ _    __        __         _     _ 
| | | | ___| | | __\ \      / /__  _ __| | __| |
| |_| |/ _ \ | |/ _ \ \ /\ / / _ \| '__| |/ _` |
|  _  |  __/ | | (_) \ V  V / (_) | |  | | (_| |
|_| |_|\___|_|_|\___/ \_/\_/ \___/|_|  |_|\__,_|                                  
 ____     __    _______    _______   __________
|     \  |  |  |  _____|  /  _____) |____  ____|
|  |\  \ |  |  | |__     (  (_____      |  |
|  | \  \|  |  |  __|     \_____  \     |  | 
|  |  \     |  | |_____    _____)  )    |  | 
|__|   \____|  |_______|  (_______/     |__| 
 
 
 


*/









vector<int> smallest_factor;
vector<bool> prime;
vector<int> primes;

void sieve(int maximum) {
    maximum = max(maximum, 1);
    smallest_factor.assign(maximum + 1, 0);
    prime.assign(maximum + 1, true);
    prime[0] = prime[1] = false;
    primes.clear();
    for (int p = 2; p <= maximum; p++)
        if (prime[p]) {
            smallest_factor[p] = p;
            primes.push_back(p);
            for (long long i = (long long)p * p; i <= maximum; i += p)
                if (prime[i]) {
                    prime[i] = false;
                    smallest_factor[i] = p;
                }
        }
}

const int N = 1e5 + 5;
VI nex(N), seen(N, N);
VVI dp(N+5, VI(20, N));
int n;
void go () {
    int n, m;
    cin >> n >> m; 
    VI nums = readVI(n);
    nex[n] = n;
    for (int i = n - 1; i >= 0; i--) {
        nex[i] = nex[i+1];
        int tmp = nums[i];
        for (auto el : primes) {
            bool x = 0;
            while(tmp % el == 0) {
                x = 1;
                tmp /= el;
            }
            if (x) {
                nex[i] = min(nex[i], seen[el]);
                seen[el] = i;
            }
        }
        if (tmp != 1) {
            nex[i] = min(nex[i], seen[tmp]);
            seen[tmp] = i;
        }
    }
    //dp[i][j] i-r 2^j
    // print(nex, n+5);
    REP(i, n) 
        dp[i][0] = nex[i];
        
    REP1(j, 20) 
    REP(i, n) 
        dp[i][j] = dp[dp[i][j-1]][j-1]; 
    
    while(m--) {
        int l, r;
        cin >> l >> r;
        l--, r--;
        int st = l, cnt = 0;
        // while(st < r) {
        // cout << st << ' ';
        for (int i = 19; i >= 0; i--) {
            if (dp[st][i] <= r) {
                st = dp[st][i];
                // cout << i << ',' << st << ' ';
                cnt += (1<<i);
            }
        }
        // }
        // cout << "\n";
        cout << cnt+1 << '\n';
    }
    // print(nex, n);
}

void init() {
    int limit = sqrt(1e5)+5;
    sieve(limit);
    // m = primes.size();
    // cout << primes.size() << '\n';
}


signed main () {

#ifdef ONLINE_JUDGE
#else
    freopen("in.txt", "r", stdin);
//	freopen("out.txt", "w", stdout);
#endif
    _upgrade
    int T = 1;
    init();
    while(T--) go();
    return 0;
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
    
*/
```