#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
//const ll mod = 1000000009;
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 4100000000000000000ll;
const ld eps = ld(0.00000000001);
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
template<class T>auto min(const T& a){ return *min_element(all(a)); }
template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
template<class T>bool chmax(T &a,const T b) { if (a<b) { a=b; return 1; } return 0;}
template<class T>bool chmin(T &a,const T b) { if (b<a) { a=b; return 1; } return 0;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}
template<class T>
struct Sum{
vector<T> data;
Sum(const vector<T>& v):data(v.size()+1){
for(ll i=0;i<v.size();i++) data[i+1]=data[i]+v[i];
}
T get(ll l,ll r) const {
return data[r]-data[l];
}
};
template<class T>
struct Sum2{
vector<vector<T>> data;
Sum2(const vector<vector<T>> &v):data(v.size()+1,vector<T>(v[0].size()+1)){
for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]=data[i][j+1]+v[i][j];
for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]+=data[i+1][j];
}
T get(ll x1,ll y1,ll x2,ll y2) const {
return data[x2][y2]+data[x1][y1]-data[x1][y2]-data[x2][y1];
}
};
void cincout(){
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout<< fixed << setprecision(15);
}
ll m;
vector<ll> p,ex;
ll Inv[100000];
struct mint{
ll v=1;
vector<ll> c;
mint(){
}
mint(ll x){
c.resize(int(p.size()));
for(int i=0;i<int(p.size());i++){
while(x%p[i]==0){
x/=p[i];
c[i]++;
}
}
v=x%m;
}
ll val(){
ll ret=v;
for(int i=0;i<int(p.size());i++){
for(int j=0;j<c[i];j++){
ret*=p[i];
ret%=m;
}
}
return ret;
}
void mul(ll x){
for(int i=0;i<int(p.size());i++){
while(x%p[i]==0){
x/=p[i];
c[i]++;
}
}
v*=x;
v%=m;
}
void mul(mint x){
for(int i=0;i<int(p.size());i++) c[i]+=x.c[i];
v*=x.v;
v%=m;
}
void inv(mint x){
for(int i=0;i<int(p.size());i++) c[i]-=x.c[i];
v*=Inv[x.v];
v%=m;
}
void inv(ll x){
for(int i=0;i<int(p.size());i++){
while(x%p[i]==0){
x/=p[i];
c[i]--;
}
}
v*=Inv[x%m];
v%=m;
}
};
struct Segtree{
ll n;
vector<mint> node;
Segtree(vector<ll> f){
ll N=f.size();
n=1;
while(n<N) n*=2;
node.resize(2*n);
for(int i=0;i<f.size();i++) node[i+n]=mint(f[i]);
for(int i=f.size();i<n;i++) node[i+n]=mint(1);
for(int j=n-1;j>=1;j--){
node[j]=node[2*j];
node[j].mul(node[2*j+1]);
}
}
void mul(int i,mint x){
i+=n;
while(i){
node[i].mul(x);
i/=2;
}
}
void inv(int i,mint x){
i+=n;
while(i){
node[i].inv(x);
i/=2;
}
}
mint prod(ll l,ll r,ll a,ll b,ll k){
if(r<=a||b<=l) return mint(1);
if(l<=a&&b<=r) return node[k];
mint x=prod(l,r,a,(a+b)/2,2*k);
x.mul(prod(l,r,(a+b)/2,b,2*k+1));
return x;
}
mint prod(ll l,ll r){
return prod(l,r,0,n,1);
}
};
int main() {
cincout();
ll n,k;
cin>>n>>k>>m;
ll C=-1;
for(int i=1;i<=m;i++) if(gcd(i,m)==1) C++;
for(int i=0;i<m;i++){
Inv[i]=modPow(i,C,m);
}
ll memo=m;
for(int i=2;i<=30000;i++){
ll cnt=0;
while(m%i==0){
m/=i;
cnt++;
}
if(cnt){
p.pb(i);
ex.pb(cnt);
}
}
m=memo;
vector<P> a(n);
for(int i=0;i<n;i++){
cin>>a[i].fi>>a[i].se;
a[i].se--;
}
sor(a);
rever(a);
vector<ll> c(k),d(k);
ll x=0;
for(int i=0;i<n;i++){
if(c[a[i].se]==0){
d[a[i].se]=x;
x++;
c[a[i].se]=1;
}
}
for(auto &e:a) e.se=d[e.se];
vector<vector<ll>> b;
for(auto &e:c) e=0;
ll ans=0;
multiset<pair<int,int>> ms;
for(int i=0;i<n;i++){
ms.insert({a[i].fi,-i});
}
ms.insert({1000000000,1000000000});
ll q=0;
//今 q 以降が f に含まれている
vector<ll> f(k);
for(int j=q;j<n;j++){
f[a[j].se]++;
}
mint ret2(1);
for(int i=1;i<k;i++){
ret2.mul(f[i]+1);
}
ll l=0;
//今 l の部分までかけている
vector<ll> ld(k);
for(auto &e:f) e++;
Segtree seg(f);
for(auto &e:f) e--;
multiset<pair<int,int>> idx;
idx.insert({n+n+n,n+n+n});
vector<vector<int>> A(k);
for(int i=0;i<n;i++) A[a[i].se].pb(i);
for(int i=0;i<n;i++){
if(c[a[i].se]==0){
ld[a[i].se]=i;
auto itr=ms.lower_bound({a[i].fi/2+1,-n-n-n});
//itr より手前の要素を使える -> itr 以下は無理
/* for(int j=q;j<=-(*itr).se;j++){
if(a[j].se>=a[i].se+1) ret2.inv(f[a[j].se]+1);
seg.inv(a[j].se,f[a[j].se]+1);
f[a[j].se]--;
seg.mul(a[j].se,f[a[j].se]+1);
if(a[j].se>=a[i].se+1) ret2.mul(f[a[j].se]+1);
}
q=-(*itr).se+1;
mint ret(1); */
//A[a[i].se] にある要素のうち、q-1 以下のもの
/*int OK=0,NG=A[a[i].se].size();
while(abs(OK-NG)>1){
int MID=(OK+NG)/2;
if(A[a[i].se][MID]<=q-1) OK=MID;
else NG=MID;
}
OK=A[a[i].se][OK];*/
//2*a[i].fi 以上の最小の idx
/*if(a[0].fi<a[OK].fi*2){
ret.mul(seg.prod(0,a[i].se));
}
else{
int ok=0,ng=a[i].se;
while(abs(ok-ng)/2){
int mid=(ok+ng)/2;
if(a[ld[mid]].fi<a[OK].fi*2) ng=mid;
else ok=mid;
}
ret.mul(seg.prod(ng,a[i].se));
}*/
ans+=(ret.val()+f[a[i].se])*(ret2.val());
ans%=m;
c[a[i].se]=1;
ret2.inv(f[a[i].se+1]+1);
}
}
cout<<ans<<endl;
}
Compilation message
fish.cpp: In constructor 'Segtree::Segtree(std::vector<long long int>)':
fish.cpp:164:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
164 | for(int i=0;i<f.size();i++) node[i+n]=mint(f[i]);
| ~^~~~~~~~~
fish.cpp: In function 'int main()':
fish.cpp:298:13: error: 'ret' was not declared in this scope; did you mean 'ret2'?
298 | ans+=(ret.val()+f[a[i].se])*(ret2.val());
| ^~~
| ret2
fish.cpp:253:6: warning: unused variable 'l' [-Wunused-variable]
253 | ll l=0;
| ^
