#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("inline") #include using namespace std; #define MD (998244353U) template struct cLtraits_identity{ using type = T; } ; template using cLtraits_try_make_signed = typename conditional< is_integral::value, make_signed, cLtraits_identity >::type; template struct cLtraits_common_type{ using tS = typename cLtraits_try_make_signed::type; using tT = typename cLtraits_try_make_signed::type; using type = typename common_type::type; } ; void*wmem; char memarr[96000000]; template inline auto max_L(S a, T b) -> typename cLtraits_common_type::type{ return (typename cLtraits_common_type::type) a >= (typename cLtraits_common_type::type) b ? a : b; } template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } template inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){ walloc1d(arr, x2-x1, mem); (*arr) -= x1; } template void sortA_L(int N, T1 a[], void *mem = wmem){ sort(a, a+N); } template void sortA_L(int N, T1 a[], T2 b[], void *mem = wmem){ int i; pair*arr; walloc1d(&arr, N, &mem); for(i=(0);i<(N);i++){ arr[i].first = a[i]; arr[i].second = b[i]; } sort(arr, arr+N); for(i=(0);i<(N);i++){ a[i] = arr[i].first; b[i] = arr[i].second; } } struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator++(){ val++; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator--(){ if(val == 0){ val = MD - 1; } else{ --val; } return *this; } inline Modint operator++(int a){ Modint res(*this); val++; if(val >= MD){ val -= MD; } return res; } inline Modint operator--(int a){ Modint res(*this); if(val == 0){ val = MD - 1; } else{ --val; } return res; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template inline T pow_L(T a, S b){ T res = 1; res = 1; for(;;){ if(b&1){ res *= a; } b >>= 1; if(b==0){ break; } a *= a; } return res; } inline double pow_L(double a, double b){ return pow(a,b); } template inline void arrInsert(const int k, int &sz, S a[], const S aval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } a[k] = aval; } template inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } for(i=sz-1;i>k;i--){ b[i] = b[i-1]; } a[k] = aval; b[k] = bval; } template inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } for(i=sz-1;i>k;i--){ b[i] = b[i-1]; } for(i=sz-1;i>k;i--){ c[i] = c[i-1]; } a[k] = aval; b[k] = bval; c[k] = cval; } template inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval, V d[], const V dval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } for(i=sz-1;i>k;i--){ b[i] = b[i-1]; } for(i=sz-1;i>k;i--){ c[i] = c[i-1]; } for(i=sz-1;i>k;i--){ d[i] = d[i-1]; } a[k] = aval; b[k] = bval; c[k] = cval; d[k] = dval; } int main(){ wmem = memarr; int N; rd(N); int K; rd(K); int M; rd(M); int L[M]; int R[M]; int cnt[K]; int i; int j; int k; int s; Modint res = 0; Modint dp[1501][1501] = {}; { int Lj4PdHRW; for(Lj4PdHRW=(0);Lj4PdHRW<(M);Lj4PdHRW++){ rd(L[Lj4PdHRW]);L[Lj4PdHRW] += (-1); rd(R[Lj4PdHRW]);R[Lj4PdHRW] += (-1); } } sortA_L(M,L,R); k = 0; for(i=(0);i<(M);i++){ if(k && L[i] == L[k-1]){ continue; } while(k && R[i] <= R[k-1]){ k--; } arrInsert(k, k, L, L[i], R, R[i]); } M = k; for(i=(0);i<(K);i++){ cnt[i] = 0; } for(i=(0);i<(M);i++){ for(j=(L[i]);j<(R[i]+1);j++){ cnt[j] = 1; } } for(i=(1);i<(K);i++){ cnt[i] += cnt[i-1]; } for(i=(0);i<(M);i++){ auto YREPHmFM = ((cnt[L[i]])- 1); auto jZyWAPpY = (( cnt[R[i]])- 1); L[i]=YREPHmFM; R[i]=jZyWAPpY; } s = 0; dp[0][0] = 1; for(k=(0);k<(M);k++){ while(s < L[k]){ for(j=(0);j<(R[k]+1);j++){ dp[s+1][j+1] += dp[s][j]; dp[s][j] = 0; } s++; } for(i=(R[k]+1)-1;i>=(s);i--){ for(j=(R[k]+1)-1;j>=(0);j--){ dp[R[k]+1][j+max_L(0, L[k]-i)] -= dp[i][j]; } } } for(i=(0);i<(K+1);i++){ for(j=(0);j<(K+1);j++){ if(dp[i][j]){ res += dp[i][j] *(pow_L(Modint(K-i+j),N)); } } } wt_L(res); wt_L('\n'); return 0; } // cLay version 20210926-1 // --- original code --- // #define MD 998244353 // int @N, @K, @M, L[M], R[M], cnt[K]; // int i, j, k, s; // Modint res = 0, dp[1501][1501] = {}; // rd((L--,R--)(M)); // sortA(M,L,R); // // k = 0; // rep(i,M){ // if(k && L[i] == L[k-1]) continue; // while(k && R[i] <= R[k-1]) k--; // arrInsert(k, k, L, L[i], R, R[i]); // } // M = k; // // rep(i,K) cnt[i] = 0; // rep(i,M) rep(j,L[i],R[i]+1) cnt[j] = 1; // rep(i,1,K) cnt[i] += cnt[i-1]; // // rep(i,M) (L[i], R[i]) = (cnt[L[i]], cnt[R[i]]) - 1; // // // wt(K); // // rep(i,M) wt(L[i], R[i]); // // s = 0; // dp[0][0] = 1; // rep(k,M){ // while(s < L[k]){ // rep(j,R[k]+1) dp[s+1][j+1] += dp[s][j], dp[s][j] = 0; // s++; // } // rrep(i,s,R[k]+1) rrep(j,R[k]+1){ // dp[R[k]+1][j+max(0,L[k]-i)] -= dp[i][j]; // } // } // // rep(i,K+1) rep(j,K+1) if(dp[i][j]){ // res += dp[i][j] * Modint(K-i+j)**N; // } // // wt(res);