#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("inline") #include using namespace std; #define MD (998244353U) 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); } int main(){ int i, loop; int N; rd(N); int K; rd(K); int A[N]; { int Lj4PdHRW; for(Lj4PdHRW=(0);Lj4PdHRW<(N);Lj4PdHRW++){ rd(A[Lj4PdHRW]); } } Modint dp[N+1]; Modint dp1[N+1]; Modint dp2[N+1]; Modint cnt[N+1]; Modint res = 0; Modint tmp; for(loop=(0);loop<(2);loop++){ int i, t; for(i=(0);i<(N+1);i++){ dp[i] = cnt[i] = 0; } cnt[0] = 1; for(t=(0);t<(K);t++){ for(i=(N)-1;i>=(0);i--){ int j; for(j=(0);j<(i);j++){ int k; cnt[i] += cnt[j] * ((pow_L(Modint(2),(t * (i-j))))); dp[i] += dp[j] * ((pow_L(Modint(2),(t * (i-j))))); for(k=(j);k<(i);k++){ dp[i] += ((pow_L(Modint(A[k]),t))) * cnt[j] * ((pow_L(Modint(2),(t * (i-j))))); } } } } if(loop==0){ for(i=(0);i<(N+1);i++){ dp1[i] = dp[i]; } } if(loop==1){ for(i=(0);i<(N+1);i++){ dp2[i] = dp[i]; } } reverse(A,A+N); } for(i=(0);i<(N);i++){ int j; for(j=(i+1);j<(N);j++){ int k; tmp = 0; for(k=(i);k<(j+1);k++){ tmp += cnt[i] * cnt[N-j-1] * ((pow_L(Modint(A[k]),K))); } tmp += dp1[i] * cnt[N-j-1]; tmp += dp2[N-1-j] * cnt[i]; res += tmp * ((pow_L(Modint(2),(K * (j-i-1))))); } } wt_L(res); wt_L('\n'); return 0; } // cLay version 20210926-1 // --- original code --- // #define MD 998244353 // int @N, @K, @A[N]; // Modint dp[N+1], dp1[], dp2[], cnt[], res = 0, tmp; // // rep(loop,2){ // rep(i,N+1) dp[i] = cnt[i] = 0; // cnt[0] = 1; // rep(t,K){ // rrep(i,N){ // rep(j,i){ // cnt[i] += cnt[j] * (Modint(2) ** (t * (i-j))); // dp[i] += dp[j] * (Modint(2) ** (t * (i-j))); // rep(k,j,i) dp[i] += (Modint(A[k]) ** t) * cnt[j] * (Modint(2) ** (t * (i-j))); // } // } // } // // if(loop==0) rep(i,N+1) dp1[i] = dp[i]; // if(loop==1) rep(i,N+1) dp2[i] = dp[i]; // reverse(A,A+N); // } // // // wt(dp1(N+1)); // // wt(dp2(N+1)); // // wt(cnt(N+1)); // // rep(i,N) rep(j,i+1,N){ // tmp = 0; // rep(k,i,j+1) tmp += cnt[i] * cnt[N-j-1] * (Modint(A[k]) ** K); // tmp += dp1[i] * cnt[N-j-1]; // tmp += dp2[N-1-j] * cnt[i]; // res += tmp * (Modint(2) ** (K * (j-i-1))); // } // // wt(res);