#pragma GCC optimize("O3") #include using namespace std; using ll=long long; using P=pair; template using V=vector; #define fi first #define se second #define all(v) (v).begin(),(v).end() const ll inf=(1e18); //const ll mod=998244353; const ll mod=1000000007; const vector dy={-1,0,1,0},dx={0,-1,0,1}; ll GCD(ll a,ll b) {return b ? GCD(b,a%b):a;} ll LCM(ll c,ll d){return c/GCD(c,d)*d;} struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout< bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; } templatevoid debag(const vector &a){cerr<<"debag :";for(auto v:a)cerr<void print(const vector &a){for(auto v:a)cout<>n; ll l=0,r=n+5; while(r-l>1){ ll mid=(l+r)/2; if((mid+1)*mid/2>=n)r=mid; else l=mid; } cout<