A

#include<bits/stdc++.h>
using namespace std;
#define int long long

const int MAXN = 200005;
int tree[MAXN << 2], lazy[MAXN << 2];
int n, m;
string s;

void push_up(int rt)
{
    tree[rt] = tree[rt << 1] + tree[rt << 1 >> 1 | 1];
}

void push_up_v2(int rt)
{
    tree[rt] = tree[rt << 1] + tree[rt << 1 | 1];
}

void build(int rt, int l, int r)
{
    lazy[rt] = 0;
    if (l == r)
    {
        tree[rt] = s[l] - '0';
        return;
    }
    int mid = (l + r) >> 1;
    build(rt << 1, l, mid);
    build(rt << 1 | 1, mid + 1, r);
    push_up_v2(rt);
}

void push_down(int rt, int l, int r)
{
    if(lazy[rt])
    {
        int mid = (l + r) >> 1;
        lazy[rt << 1] ^= 1;
        tree[rt << 1] = (mid - l + 1) - tree[rt << 1];
        lazy[rt << 1 | 1] ^= 1;
        tree[rt << 1 | 1] = (r - mid) - tree[rt << 1 | 1];
        lazy[rt] = 0;
    }
}

void update(int rt, int l, int r, int ql, int qr)
{
    if(ql <= l && r <= qr)
    {
        tree[rt] = (r - l + 1) - tree[rt];
        lazy[rt] ^= 1;
        return;
    }
    push_down(rt, l, r);
    int mid = (l + r) >> 1;
    if(ql <= mid)
    	update(rt << 1, l, mid, ql, qr);
    if(qr > mid)
    	update(rt << 1 | 1, mid + 1, r, ql, qr);
    push_up_v2(rt);
}

signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    cin >> n >> m >> s;
    s = ' ' + s;
    build(1, 1, n);
    while(m--)
    {
        int x, l, r;
        cin >> x >> l >> r;
        if(x == 1)
        {
            update(1, 1, n, l, r);
        }
        else
        {
            int sum = tree[1];
            int res = max(0LL, min(r, sum) - l + 1);
            cout << res << endl;
        }
    }
    return 0;
}

B

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n, k;
int d[35], pos[35];
void insert(int v, int p)
{
    for(int i = 30; i >= 0; i--)
    {
        if((v >> i) & 1)
        {
            if(!d[i])
            {
                d[i] = v;
                pos[i] = p;
                return;
            }
            if(pos[i] < p)
            {
                swap(pos[i], p);
                swap(d[i], v);
            }
            v ^= d[i];
        }
    }
}
int query(int L)
{
    int res = 0;
    for(int i = 30; i >= 0; i--)
    {
        if(pos[i] >= L) {
            if((res ^ d[i]) > res)
            {
                res ^= d[i];
            }
        }
    }
    return res;
}
signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    cin >> n >> k;
    int ans = 1e9, L = 1;
    for(int i = 1; i <= n; i++)
    {
        int x;
        cin >> x;
        insert(x, i);
        while(L <= i && query(L) >= k)
        {
            ans = min(ans, i - L + 1);
            L++;
        }
    }
    if(ans > n)
    	cout << -1 << '\n';
    else
    	cout << ans << '\n';
    return 0;
}

C

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n, m;
vector<int> a;
int sum;
int f[1000005];
int find(int x)
{
    return f[x] == x ? x : f[x] = find(f[x]);
}
signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    int n, m;
    cin >> n >> m;
    vector<int> a;
    int sum = 0;
    for(int i = 1; i <= n; i++)
    {
        int x;
        cin >> x;
        if(x <= m) a.push_back(x);
        else sum += x;
    }
    if(sum)
    {
        cout << 0;
        return 0;
    }
    for(int i = 0; i <= m; i++)
        f[i] = i;
    int cnt = 0;
    for(int x : a)
    {
        for(int k = 1; k <= x; k++)
        {
            int u = m + 1 - (m * k + x - 1) / x;
            if(u <= 0) break;
            int p = find(u);
            if(p > 0)
            {
                cnt++;
                f[p] = find(p - 1);
            }
            else
            {
                break;
            }
        }
    }
    
    cout << m - cnt << '\n';
    return 0;
}

D

#include<bits/stdc++.h>
#define int long long
int n;
using namespace std;
string s = " ", ss;
int ans = 0;
signed main()
{
    cin >> n;
    cin >> ss;
    s += ss;
    for(int i = 4; i <= n; i ++)
    {
    	if(s[i - 1] == '2' && s[i - 2] == '0' && s[i - 3] == '2')
    	{
    		ans ++;
    		s[i] = '6';
    	}
    }
    cout << ans;
    return 0;
}

E

#include<bits/stdc++.h>
#define int long long
#define inv(x) ksm(x, mod - 2)
using namespace std;
const int mod = 998244353;
int T;
int n, m, minv;
int dp[200003];
int d[200003];
int ksm(int x, int y)
{
    int ans = 1;
    while(y)
    {
        if(y & 1)
        {
            ans = ans * x % mod;
        }
        x = x * x % mod;
        y >>= 1;
    }
    return ans;
}
signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    cin >> T;
    while(T --)
    {
        cin >> n >> m;
        minv = inv(m);
        for(int i = 1; i <= m; i ++)
        {
            dp[i] = m;
            d[i] = d[i - 1] + dp[i];
            d[i] %= mod;
        }
        for(int i = m + 1; i <= n; i ++)
        {
            dp[i] = 1;
            dp[i] += minv * (d[i - 1] - d[i - m - 1] + mod) % mod;
            dp[i] %= mod;
            d[i] = d[i - 1] + dp[i];
            d[i] %= mod;
        }
        cout << dp[n] << endl;
    }
    return 0;
}

F

#include<bits/stdc++.h>
#define int long long
using namespace std;
int a[233] = {0, 1, 1}, n;
signed main()
{
    cin >> n;
    for(int i = 3; i <= n; i ++)
    {
        a[i] = a[i - 1] + a[i - 2] + 1;
    }
    cout << a[n] << endl;
    return 0;
}

G

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n;
signed main()
{
    cin >> n;
    cout << (n - 1 + (n - 1) % 2) * ((n + 1) / 2) / 2 << endl;
    for(int i = 1, j = n - 1; i <= n, j >= 1; i ++, j -= 2)
    {
        for(int k = 1; k <= j; k ++)
        {
            cout << i << ' ' << i + k << endl;
        }
    }
    return 0;
}

H

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n, a, cnt;
signed main()
{
    cin >> n;
    for(int i = 1; i <= n; i ++)
    {
        cin >> a;
        if(a >= 6)
            cnt ++;
    }
    cout << cnt;
    return 0;
}

I

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n;
int p[200003], pcnt;
int minp[200003] = {1, 1};
struct node
{
    int num;
    vector<pair<int, int> > cnt;
}a[200003];
bool cmp(node a, node b)
{
    int i = 0, j = 0;
    while(i < a.cnt.size() && j < b.cnt.size())
    {
        if(a.cnt[i].first == b.cnt[j].first)
        {
            if(a.cnt[i].second == b.cnt[j].second)
            {
                i ++;
                j ++;
            }
            else
            {
                return a.cnt[i].second < b.cnt[j].second;
            }
        }
        else
        {
            return a.cnt[i].first > b.cnt[j].first;
        }
    }
    return b.cnt.size() - j;
}
signed main()
{
    for(int i = 2; i <= 200000; i ++)
    {
        if(minp[i] == 0)
        {
            minp[i] = i;
            p[++ pcnt] = i;
        }
        for(int j = 1; j <= pcnt && i * p[j] <= 200000; j ++)
        {
            minp[i * p[j]] = p[j];
            if(i % p[j] == 0)
            {
                break;
            }
        }
    }
    cin >> n;
    for(int i = 1; i <= n; i ++)
    {
        int sum = i;
        a[i].num = i;
        while(sum > 1)
        {
            int pp = minp[sum];
            int ppcnt = 0;
            while(sum % pp == 0)
            {
                ppcnt ++;
                sum /= pp;
            }
            int ppsum = 0;
            for(int j = 0; j <= 5; j ++)
            {
                if((ppcnt >> j) & 1)
                {
                    ppsum += (1 << (5 - j));
                }
            }
            a[i].cnt.push_back({pp, ppsum});
            // cout << i << ' ' << pp << ' ' << ppcnt << ' ' << ppsum << endl;
        }
    }
    sort(a + 1, a + 1 + n, cmp);
    for(int i = 1; i <= n; i ++)
    {
        cout << a[i].num << ' ';
    }
}

J

#include<bits/stdc++.h>
#define int long long
using namespace std;
int n, T;
void solve() {
    int n;
    cin >> n;
    vector<int> pos(n + 1);
    for(int i = 1; i <= n; i++)
    {
        int x;
        cin >> x;
        pos[x] = i;
    }
    for(int p = 2; p * p <= n; p++)
    {
        for(int q = 1; q < p; q++)
        {
            if(__gcd(p, q) == 1)
            {
                for(int a = 1; a * p * p <= n; a ++)
                {
                    int v1 = a * q * q;
                    int v2 = a * p * q;
                    int v3 = a * p * p;
                    if((pos[v1] < pos[v2] && pos[v2] < pos[v3]) || 
                       (pos[v3] < pos[v2] && pos[v2] < pos[v1]))
                    {
                        cout << "No\n";
                        return;
                    }
                }
            }
        }
    }
    cout << "Yes\n";
}

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    cin >> T;
    while(T --)
    {
        solve();
    }
    return 0;
}