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zc
2020-03-07 21:58:00
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\overbrace{111\dots111}^{\text{N个1}} \equiv k \pmod m \\ \frac{10^N-1}9\equiv k \pmod m \\ 10^N\equiv 9k+1 \pmod m

顺利地推出是bsgs,(m是质数,也就不用exbsgs了)

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define register
    #define ll __int128
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i(x);i<=y;++i)
    #define Fdr(i,x,y) for(int i(x);i>=y;--i)
    #define fl(i,x) for(int i(head[x]),to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) ((int)(log2(n)))
    #define inf 2122219134
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const int str=1<<20;static char in_buf[str],*in_s,*in_t;bool __=0;il char gc(){return (in_s==in_t)&&(in_t=(in_s=in_buf)+fread(in_buf,1,str,stdin)),in_s==in_t?EOF:*in_s++;}il void in(string &ch){ch.clear();if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)__=1;}il void in(char &ch){if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)__=1;else ch=c;}il void in(char *ch){*ch='\0';if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)__=1;*ch='\0';}template<typename T>il void in(T &x){if(__)return;char c=gc();bool f=0;while(c!=EOF&&(c<'0'||c>'9'))f^=(c=='-'),c=gc();if(c==EOF){__=1;return;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=x*10+c-48,c=gc();if(c==EOF)__=1;if(f)x=-x;}template<typename T,typename ... arr>il void in(T &x,arr & ... y){in(x),in(y...);}const char ln='\n';static char out_buf[str],*out_s=out_buf,*out_t=out_buf+str;il void flush(){fwrite(out_buf,1,out_s-out_buf,stdout);out_s=out_buf;}il void pt(char c){(out_s==out_t)?(fwrite(out_s=out_buf,1,str,stdout),*out_s++=c):(*out_s++=c);}il void out(const char* s){while(*s)pt(*s++);}il void out(char* s){while(*s)pt(*s++);}il void out(char c){pt(c);}il void out(string s){for(int i=0;s[i];i++)pt(s[i]);}template<typename T>il void out(T x){if(!x){pt('0');return;}if(x<0)pt('-'),x=-x;char a[50],t=0;while(x)a[t++]=x%10,x/= 10;while(t--)pt(a[t]+'0');}template<typename T,typename ... arr>il void out(T x,arr & ... y){out(x),out(y...);}}using namespace IO;
const int N=10000007;
// struct hash{
//     struct edge{int nxt;ll to,w;}e[N];
//     int head[N],cnt=0;
//     il void add(int x,ll y,ll w){e[++cnt].to=y;e[cnt].nxt=head[x];head[x]=cnt;e[cnt].w=w;}
//     il void ins(ll x,ll v){add(x%N,x,v);}
//     il ll ask(ll x){fl(i,x%N)if(to==x)return e[i].w;return -1;}
// }S;
map<ll,ll>S;
il ll pw(ll x,ll b,ll p){
    ll ans=1;
    while(b){
        if(b&1)ans=ans*x%p;
        b>>=1;x=x*x%p;
    }
    return ans;
}
ll bsgs(ll y,ll z,ll p){
    y%=p;z%=p;
    if(!y){if(!z)return 1;return -1;}
    ll m=(ll)sqrt((db)p)+1,x=z%p,t=pw(y,m,p);
    Fur(i,0,m)S[x]=i+1,x=x*y%p;
    x=1;
    Fur(i,1,m){
        x=x*t%p;
        ll k=S[x]-1;
        if(~k)return ((i*m-k)%p+p)%p;
    }
    return -1;
}
int main(){
    ll k,m;
    in(k,m);
    printf("%lld\n",bsgs(10,9*k+1,m));
}
LG 4884 多少个1
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