#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("inline") #include using namespace std; 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 min_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; } 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; } } inline void rd(long long &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(long long x){ int s=0; int m=0; char f[20]; 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(const char c[]){ int i=0; for(i=0;c[i]!='\0';i++){ my_putchar_unlocked(c[i]); } } 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; } template struct DijkstraHeap{ int*hp; int*place; int size; char*visited; T*val; void malloc(int N){ hp = (int*)std::malloc(N*sizeof(int)); place = (int*)std::malloc(N*sizeof(int)); visited = (char*)std::malloc(N*sizeof(char)); val = (T*)std::malloc(N*sizeof(T)); } void free(){ std::free(hp); std::free(place); std::free(visited); std::free(val); } void walloc(int N, void **mem=&wmem){ walloc1d(&hp, N, mem); walloc1d(&place, N, mem); walloc1d(&visited, N, mem); walloc1d(&val, N, mem); } void malloc(int N, int init_fg){ malloc(N); if(init_fg){ init(N); } } void walloc(int N, int init_fg, void **mem=&wmem){ walloc(N,mem); if(init_fg){ init(N); } } void init(int N){ int i; size = 0; for(i=(0);i<(N);i++){ place[i]=-1; } for(i=(0);i<(N);i++){ visited[i]=0; } } void up(int n){ int m; while(n){ m=(n-1)/2; if(val[hp[m]]<=val[hp[n]]){ break; } swap(hp[m],hp[n]); swap(place[hp[m]],place[hp[n]]); n=m; } } void down(int n){ int m; for(;;){ m=2*n+1; if(m>=size){ break; } if(m+1val[hp[m+1]]){ m++; } if(val[hp[m]]>=val[hp[n]]){ break; } swap(hp[m],hp[n]); swap(place[hp[m]],place[hp[n]]); n=m; } } void change(int n, T v){ if(visited[n]||(place[n]>=0&&val[n]<=v)){ return; } val[n]=v; if(place[n]==-1){ place[n]=size; hp[size++]=n; up(place[n]); } else{ up(place[n]); } } int pop(void){ int res=hp[0]; place[res]=-1; size--; if(size){ hp[0]=hp[size]; place[hp[0]]=0; down(0); } visited[res]=1; return res; } } ; struct graph{ int N; int*es; int**edge; void setDirectEdge(int N__, int M, int A[], int B[], void **mem = &wmem){ int i; N = N__; walloc1d(&es, N, mem); walloc1d(&edge, N, mem); walloc1d(&edge[0], M, mem); for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ es[A[i]]++; } for(i=(0);i<(N);i++){ walloc1d(&edge[i], es[i], mem); } for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ edge[A[i]][es[A[i]]++] = B[i]; } } graph reverse(void **mem = &wmem){ int i; int j; int k; graph g; g.N = N; walloc1d(&g.es, N, mem); walloc1d(&g.edge, N, mem); for(i=(0);i<(N);i++){ g.es[i] = 0; } for(i=(0);i<(N);i++){ for(j=(0);j<(es[i]);j++){ g.es[edge[i][j]]++; } } for(i=(0);i<(N);i++){ walloc1d(&g.edge[i], g.es[i], mem); } for(i=(0);i<(N);i++){ g.es[i] = 0; } for(i=(0);i<(N);i++){ for(j=(0);j<(es[i]);j++){ k = edge[i][j]; g.edge[k][g.es[k]++] = i; } } return g; } void getDist(int root, int res[], void *mem = wmem){ int i; int j; int k; int*q; int s; int z; walloc1d(&q, N, &mem); for(i=(0);i<(N);i++){ res[i]=-1; } res[root]=0; s=0; z=1; q[0]=root; while(z){ i=q[s++]; z--; for(j=(0);j<(es[i]);j++){ k=edge[i][j]; if(res[k]>=0){ continue; } res[k]=res[i]+1; q[s+z++]=k; } } } int getDist(int a, int b, void *mem = wmem){ int i; int j; int k; int*q; int s; int z; int*d; if(a==b){ return 0; } walloc1d(&d, N, &mem); walloc1d(&q, N, &mem); for(i=(0);i<(N);i++){ d[i] = -1; } d[a] = 0; s = 0; z = 1; q[0] = a; while(z){ i = q[s++]; z--; for(j=(0);j<(es[i]);j++){ k = edge[i][j]; if(d[k] >= 0){ continue; } d[k] = d[i] + 1; if(k==b){ return d[k]; } q[s+z++] = k; } } return -1; } } ; template struct wgraph{ int N; int*es; int**edge; T**cost; graph g; void setDirectEdge(int N__, int M, int A[], int B[], T C[], void **mem = &wmem){ int i; N = N__; walloc1d(&es, N, mem); for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ es[A[i]]++; } walloc1d(&edge, N, mem); for(i=(0);i<(N);i++){ walloc1d(&edge[i], es[i], mem); } walloc1d(&cost, N, mem); for(i=(0);i<(N);i++){ walloc1d(&cost[i], es[i], mem); } for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ edge[A[i]][es[A[i]]] = B[i]; cost[A[i]][es[A[i]]++] = C[i]; } g.N = N; g.es = es; g.edge = edge; } template void getDist(int root, S res[], S unreachable = -1, void *mem = wmem){ int i; int j; DijkstraHeap hp; hp.walloc(N, &mem); hp.init(N); hp.change(root,0); while(hp.size){ i = hp.pop(); for(j=(0);j<(es[i]);j++){ hp.change(edge[i][j], hp.val[i]+cost[i][j]); } } for(i=(0);i<(N);i++){ res[i] = (hp.visited[i] ? hp.val[i] : unreachable); } } } ; int N; int S; int T; int K; int M; int A[200000]; int B[200000]; long long X[200000]; long long Y[200000]; int nn; int mm; int aa[2000000]; int bb[2000000]; long long cc[2000000]; long long d[2000000]; int bk[2000000]; int ress; int res[2000000]; wgraph g; int main(){ int i, k; wmem = memarr; rd(N); rd(S);S += (-1); rd(T);T += (-1); rd(K); { int Lj4PdHRW; for(Lj4PdHRW=(0);Lj4PdHRW<(N);Lj4PdHRW++){ rd(X[Lj4PdHRW]); } } rd(M); { int e98WHCEY; for(e98WHCEY=(0);e98WHCEY<(M);e98WHCEY++){ rd(A[e98WHCEY]);A[e98WHCEY] += (-1); rd(B[e98WHCEY]);B[e98WHCEY] += (-1); rd(Y[e98WHCEY]); } } for(i=(0);i<(M);i++){ Y[i] += X[B[i]]; } nn = N * K; for(k=(0);k<(K);k++){ for(i=(0);i<(M);i++){ arrInsert(mm, mm, aa, N*k+A[i], bb, N*min_L(K-1, k+1)+B[i], cc, Y[i]); } } g.setDirectEdge(nn,mm,aa,bb,cc); g.getDist(S,d); if(d[(K-1)*N+T] == -1){ wt_L("Impossible"); wt_L('\n'); return 0; } wt_L("Possible"); wt_L('\n'); wt_L(d[(K-1)*N+T]+X[S]); wt_L('\n'); for(i=(0);i<(nn);i++){ if(d[i] >= 0){ int j; for(j=(0);j<(g.es[i]);j++){ if(d[g.edge[i][j]] == d[i]+g.cost[i][j]){ bk[g.edge[i][j]] = i; } } } } i = (K-1) * N + T; for(;;){ res[ress++] = i % N; if(i == S){ break; } i = bk[i]; } reverse(res,res+ress); wt_L(ress); wt_L('\n'); { int jbtyPBGc; if(ress==0){ wt_L('\n'); } else{ for(jbtyPBGc=(0);jbtyPBGc<(ress-1);jbtyPBGc++){ wt_L(res[jbtyPBGc]+1); wt_L(' '); } wt_L(res[jbtyPBGc]+1); wt_L('\n'); } } return 0; } // cLay version 20210611-1 [beta] // --- original code --- // int N, S, T, K, M, A[2d5], B[]; // ll X[], Y[]; // int nn, mm, aa[2d6], bb[]; ll cc[], d[]; // int bk[], ress, res[]; // wgraph g; // { // rd(N,S--,T--,K,X(N),M,(A--,B--,Y)(M)); // rep(i,M) Y[i] += X[B[i]]; // // nn = N * K; // rep(k,K) rep(i,M) arrInsert(mm, mm, aa, N*k+A[i], bb, N*min(K-1,k+1)+B[i], cc, Y[i]); // g.setDirectEdge(nn,mm,aa,bb,cc); // g.getDist(S,d); // // if(d[(K-1)*N+T] == -1) wt("Impossible"), return 0; // wt("Possible"); // wt(d[(K-1)*N+T]+X[S]); // // rep(i,nn) if(d[i] >= 0) rep(j,g.es[i]) if(d[g.edge[i][j]] == d[i]+g.cost[i][j]) bk[g.edge[i][j]] = i; // i = (K-1) * N + T; // for(;;){ // res[ress++] = i % N; // if(i == S) break; // i = bk[i]; // } // reverse(res,res+ress); // wt(ress); // wt(res(ress)+1); // }