#include using namespace std; using ll = long long; const int iinf = 1e9; const ll inf = 1e18; template struct Mint { using M=Mint; ll v; M& put(ll x) { v=(x>=1; } return res; } M inv() { return pow(mod-2); } }; template ostream&operator<<(ostream&o,Mintv){return o< ostream& operator<<(ostream &o, vector v) { for (int i = 0; i < v.size(); i++) o << v[i] << (i+1 struct SegTree { using F = function; int n; F f; T ti; vector dat; SegTree() {} SegTree(F f, T ti,int num) : f(f), ti(ti) { n = max(__bit_ceil(num), 1); dat.assign(n << 1, ti); } SegTree(F f,T ti,vector&v):SegTree(f,ti,v.size()){ for (int i = 0; i < v.size(); i++) dat[n + i] = v[i]; for(int i=n-1;i;i--) dat[i]=f(dat[i*2], dat[i*2+1]); } void set_val(int k, T x) { dat[k += n] = x; while(k >>= 1) dat[k] = f(dat[k*2], dat[k*2+1]); } T query(int a, int b) { if (a >= b) return ti; T vl = ti, vr = ti; for (int l=a+n, r=b+n; l>=1, r>>=1) { if (l & 1) vl = f(vl, dat[l++]); if (r & 1) vr = f(dat[--r], vr); } return f(vl, vr); } }; struct Edge { int to; ll cost; }; const int MOD = 998244353; // a^e mod ll modpow(ll a, ll e=MOD-2){ ll r=1; while(e){ if(e&1) r=r*a%MOD; a=a*a%MOD; e>>=1; } return r; } int main() { cin.tie(0)->sync_with_stdio(false); int N, M; cin >> N >> M; vector A(N+1); for(int i=1;i<=N;i++){ cin >> A[i]; } // DP[i&1][t][p]: 長さ i まで見て、 // prefix-zero の回数が t, 現在の prefix-parity が p(0 or 1) // となる y_1..y_i の (-1)^{y·A} の総和 vector< vector> > dp(2, vector>(N+2, {0,0})); dp[0][1][0] = 1; // i=0: prefix[0]=0 なのでゼロ回数=1, parity=0 for(int i=1;i<=N;i++){ auto &cur = dp[(i-1)&1]; auto &nxt = dp[i&1]; // clear for(int t=1;t<=i+1;t++) nxt[t][0]=nxt[t][1]=0; // 遷移 // y_i = 0: prefix は変わらず p, new_t = t + (p==0), weight = +1 // y_i = 1: prefix flips to 1-p, new_t = t + ((1-p)==0), // weight = (-1)^{A_i} ll w1 = (A[i]==1 ? MOD-1 : 1); for(int t=1;t<=i;t++){ for(int p=0;p<2;p++){ ll v = cur[t][p]; if(!v) continue; // case y=0 int np = p; int nt = t + (np==0); nxt[nt][np] = (nxt[nt][np] + v) % MOD; // case y=1 np = 1-p; nt = t + (np==0); nxt[nt][np] = (nxt[nt][np] + v * w1) % MOD; } } // swap done by toggling i&1 } // C[t] = dp[N&1][t][0] + dp[N&1][t][1] vector C(N+2,0); for(int t=1;t<=N+1;t++){ C[t] = (dp[N&1][t][0] + dp[N&1][t][1]) % MOD; } // 2^{-N} mod ll inv2 = (MOD+1)/2; ll inv2N = modpow(inv2, N); // 前半 P = N(N+1)/2 mod ll P = (ll)N * (N+1) % MOD * modpow(2) % MOD; // T(t) = 2*(t^2 - (N+1)t) + P auto T = [&](int t)->ll{ ll tt = ( (ll)t * t % MOD - (ll)(N+1) * t % MOD + MOD ) % MOD; return ( (2*tt)%MOD + P ) % MOD; }; ll ans = 0; for(int t=1;t<=N+1;t++){ if(C[t]==0) continue; ll w = modpow(T(t), M); ans = (ans + C[t] * w) % MOD; } // 最後に 2^{-N} をかけて完成 ans = ans * inv2N % MOD; cout << ans << "\n"; return 0; }