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#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll L,a,b,mod;
struct Matric
{
ll a[3][3];
Matric(){memset(a,0,sizeof(a));}
Matric operator*(const Matric&o)const
{
Matric ans;
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
for(int k=0;k<3;k++)
{
ans.a[i][j]=(ans.a[i][j]+a[i][k]*o.a[k][j]%mod)%mod;
}
return ans;
}
};
Matric Mqpow(Matric a,ll n)
{
Matric base=a;
Matric ans;
ans.a[0][0]=1,ans.a[1][1]=1,ans.a[2][2]=1;
while(n)
{
if(n&1)
ans=ans*base;
base=base*base;
n>>=1;
}
return ans;
}
ll qpow(ll a,ll n)
{
ll base=a;
ll ans=1;
while(n)
{
if(n&1)
ans=ans*base%mod;
base=base*base%mod;
n>>=1;
}
return ans;
}
int getlen(ll x)
{
int ans=0;
while(x)
{
x/=10;
ans++;
}
return ans;
}
ll getpos(int x)
{
ll l=1,r=L,ans=1;;
while(l<=r)
{
ll m=l+r>>1;
if(getlen(a+b*(m-1))<=x) l=m+1,ans=m;
else r=m-1;
}
return ans;
}
int main()
{
scanf("%lld%lld%lld%lld",&L,&a,&b,&mod);
ll ans=a%mod;
ll res=a%mod;
ll now=1;
for(int i=1;i<=18;i++)
{
ll p=getpos(i);
if(p==now) continue;
Matric A;
A.a[0][0]=qpow(10,i),A.a[0][1]=1,A.a[0][2]=1;
A.a[1][1]=1,A.a[1][2]=1,A.a[2][2]=1;
A=Mqpow(A,p-now);
ans=(A.a[0][0]*ans%mod+A.a[0][1]*res%mod+b%mod*A.a[0][2]%mod)%mod;
res=(res+b%mod*(p-now)%mod)%mod;
now=p;
}
printf("%lld\n",ans);
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using vi = vector<int>;
using vl = vector<ll>;
using _loop_int = int;
#define REP(i,n) for(_loop_int i=0; i<(_loop_int)(n); i++)
#define FOR(i,a,b) for(_loop_int i=(_loop_int)(a); i<(_loop_int)(b); i++)
#define FORR(i,a,b) for(_loop_int i=(_loop_int)(b)-1; i>=(_loop_int)(a); i--)
#define CHMIN(a,b) (a)=min((a),(b))
#define CHMAX(a,b) (a)=max((a),(b))
#define ALL(v) (v).begin(),(v).end()
#define DEBUG(x) cerr<<#x<<": "<<(x)<<endl
#define DEBUG_VEC(v) cerr<<#v<<": ";REP(__i,(v).size())cerr<<((v)[__i])<<", ";cerr<<endl
ll l,a,b,m;
ll modpow(ll a, ll b, ll m){
ll r = 1;
a %= m;
while(b){
if(b&1)r=r*a%m;
a=a*a%m;
b>>=1;
}
return r;
}
ll calc1(ll n, ll r){
if(n<=4){
ll ret = 0;
ll x = 1;
REP(i,n){
ret += x;
ret %= m;
x = x * r % m;
}
return ret;
}else{
if(n%2==0){
return calc1(n/2,r)*(1+modpow(r,n/2,m))%m;
}else{
return (calc1(n/2,r)*(1+modpow(r,n/2,m))%m + modpow(r,n-1,m)) % m;
}
}
}
ll calc2(ll n, ll r){
if(n<=4){
ll ret = 0;
ll x = 1;
r %= m;
REP(i,n){
ret += x*i%m;
ret %= m;
x = x * r % m;
}
return ret;
}else{
ll ret = 0;
ll n2 = n/2;
ret += calc2(n2,r)*(1+modpow(r,n2,m))%m;
ret %= m;
ret += n2%m*modpow(r,n2,m)%m*calc1(n2,r)%m;
ret %= m;
if(n%2==1){
ret += (n-1)%m*modpow(r,n-1,m)%m;
ret %= m;
}
return ret;
}
}
ll solve(ll n, ll a, ll b, int len){
if(n<=0)return 0;
ll thr = 1;
REP(i,len)thr *= 10;
ll ng = -1, ok = n;
while(ng+1<ok){
ll x = (ok+ng)/2;
(a+b*x>=thr ? ok : ng) = x;
}
if(ok==n){
return solve(n,a,b,len-1);
}
thr = thr%m*10%m;
ll n2 = n-ok;
ll add = modpow(thr,n2,m) * solve(ok,a,b,len-1) % m;
a = (a + b * (n-1)) % m;
b = m-b%m;
add += a * calc1(n2,thr) % m;
add += b * calc2(n2,thr) % m;
return add % m;
}
int main(){
cin>>l>>a>>b>>m;
ll ans = solve(l,a,b,18);
cout<<ans<<endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
int digit(int64_t x){
int ret = 0;
for(;x>0;ret++) x /= 10;
return ret;
}
void matpow(const int64_t *X, int64_t *ans, int64_t n, int64_t mod){
if(n==0){
for(int i=0;i<3;i++){
for(int j=0;j<3;j++){
ans[i*3+j] = (i==j ? 1 : 0);
}
}
}else if(n==1){
for(int i=0;i<9;i++) ans[i] = X[i] % mod;
}else if(n%2 == 0){
int64_t XX[9];
for(int i=0;i<3;i++){
for(int k=0;k<3;k++){
XX[i*3+k] = 0;
for(int j=0;j<3;j++){
XX[i*3+k] = (XX[i*3+k] + X[i*3+j] * X[j*3+k] % mod) % mod;
}
}
}
matpow(XX, ans, n/2, mod);
}else{
int64_t XX[9];
for(int i=0;i<3;i++){
for(int k=0;k<3;k++){
XX[i*3+k] = 0;
for(int j=0;j<3;j++){
XX[i*3+k] = (XX[i*3+k] + X[i*3+j] * X[j*3+k] % mod) % mod;
}
}
}
matpow(XX, ans, n/2, mod);
for(int i=0;i<9;i++){
XX[i] = ans[i];
ans[i] = 0;
}
for(int i=0;i<3;i++){
for(int k=0;k<3;k++){
for(int j=0;j<3;j++){
ans[i*3+k] = (ans[i*3+k] + XX[i*3+j] * X[j*3+k] % mod) % mod;
}
}
}
}
}
int main(){
int64_t L, A, B, M;
cin >> L >> A >> B >> M;
pair<int64_t,int64_t> pos[19];
for(int i=1;i<=18;i++){
int64_t l = -1, r = L;
while(r-l > 1){
int64_t m = (l+r) / 2;
if(digit(A + m*B) < i) l = m;
else r = m;
}
pos[i].first = r;
l = -1; r = L;
while(r-l > 1){
int64_t m = (l+r) / 2;
if(digit(A + m*B) <= i) l = m;
else r = m;
}
pos[i].second = r;
}
A %= M; B %= M;
int64_t s = 0, n = A, d = 1;
for(int i=1;i<=18;i++){
d *= 10;
int64_t X[9] = {0}, Xp[9];
X[0] = d % M;
X[1] = X[4] = X[5] = X[8] = 1;
matpow(X, Xp, pos[i].second - pos[i].first, M);
s = (Xp[0]*s%M + Xp[1]*n%M + Xp[2]*B%M) % M;
n = (Xp[3]*s%M + Xp[4]*n%M + Xp[5]*B%M) % M;
}
cout << s << endl;
return 0;
} |
#include "bits/stdc++.h"
using namespace std;
typedef vector<long long> vec;
typedef vector<vec> mat;
mat Mul(mat& A, mat& B, long long MOD) {
mat C(A.size(), vec(B.front().size()));
for (int i = 0; i < A.size(); i++) {
for (int k = 0; k < B.size(); k++) {
for (int j = 0; j < B.front().size(); j++) {
C[i][j] += ((A[i][k] % MOD) * (B[k][j] % MOD) % MOD);
C[i][j] = C[i][j] % MOD;
}
}
}
return C;
}
mat Calc(mat A, long long N, long long M) {
if (N == 1) return A;
if (N % 2 == 0) {
mat B = Calc(A, N / 2, M);
return Mul(B, B, M);
}
mat B = Calc(A, N - 1, M);
return Mul(B, A, M);
}
int main() {
long long L, A, B, C[18], M, COUNT;
mat P(1, vec(3));
cin >> L >> A >> B >> M;
COUNT = L;
P[0][0] = 0, P[0][1] = A, P[0][2] = 1;
for (int i = 0; i < 18; i++) {
long long N1 = 1, N2 = 1;
for (int j = 0; j < i; j++) N1 *= 10, N2 *= 10;
N2 *= 10;
N1--, N2--;
if (N2 < A || COUNT == 0) {
C[i] = 0;
continue;
}
else if (N1 < A) {
C[i] = (N2 - A) / B + 1;
}
else {
C[i] = (N2 - A) / B - (N1 - A) / B;
}
if (COUNT < C[i]) C[i] = COUNT, COUNT = 0;
else COUNT -= C[i];
}
for (int i = 0; i < 18; i++) {
if (C[i] == 0) continue;
mat Q(3, vec(3));
Q[0][0] = (long long)pow(10, i + 1) % M, Q[0][1] = 0, Q[0][2] = 0;
Q[1][0] = 1, Q[1][1] = 1, Q[1][2] = 0;
Q[2][0] = 0, Q[2][1] = B % M, Q[2][2] = 1;
mat R(3, vec(3));
R = Calc(Q, C[i], M);
P = Mul(P, R, M);
}
cout << P[0][0];
} |
#include <bits/stdc++.h>
#define rep(i,n) for(int i=0; i<(n); i++)
#define int long long
#define double long double
#define P pair<long long,long long>
#define all(a) a.begin(),a.end()
#define INF 10000000000000000
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
int mod;
template <typename T>
using Matrix = vector<vector<T>>;
template <typename T>
void init_mat(Matrix<T> &A, int h, int w){
A.resize(h,vector<T>(w,0));
}
template <typename T>
Matrix<T> calc_mat(Matrix<T> A, Matrix<T> B){
Matrix<T> C(A.size(),vector<T>(B[0].size()));
for(int i=0; i<A.size(); i++){
for(int k=0; k<B.size(); k++){
for(int j=0; j<B[0].size(); j++){
C[i][j]=(C[i][j]+A[i][k]*B[k][j])%mod;
}
}
}
return C;
}
template <typename T>
Matrix<T> pow_mat(Matrix<T> A, int pow){
Matrix<T> B(A.size(),vector<T>(A.size()));
for(int i=0; i<A.size(); i++)B[i][i]=1;
while(pow>0){
if(pow%2==1)B=calc_mat(B, A);
A=calc_mat(A, A);
pow/=2;
}
return B;
}
signed main(void){
cin.tie(0); cout.tie(0);
ios::sync_with_stdio(false);
int L,A,B,M; cin>>L>>A>>B>>M;
mod=M; int cur10=1,ans=0;
rep(i,18){
int fir=max<int>(A,A+(cur10-A+B-1)/B*B);
cur10*=10;
int las=min<int>(A+(L-1)*B,A+(cur10-A+B-1)/B*B-B);
int num=(las-fir)/B+1;
if(num<=0)continue;
Matrix<int> mat1,mat2;
init_mat(mat1,1,3); init_mat(mat2,3,3);
mat1[0][0]=ans; mat1[0][1]=fir%mod; mat1[0][2]=1;
mat2[0][0]=cur10%mod; mat2[0][1]=mat2[0][2]=mat2[1][2]=mat2[2][0]=0;
mat2[1][0]=mat2[1][1]=mat2[2][2]=1; mat2[2][1]=B%mod;
mat2=pow_mat(mat2,num);
mat1=calc_mat(mat1,mat2);
ans=mat1[0][0];
}
cout<<ans<<endl;
} |
/// However long the night,
/// The dawn will break
/// ICPC next year
#include<bits/stdc++.h>
using namespace std ;
const int N = 1e5+5 ;
unsigned long long l ,a ,b ,mod ;
typedef vector<unsigned long long> vll ;
typedef vector<vll> vvll ;
#define Sz(matrix ,n ,m) matrix.assign(n, vll(m));
vvll matrixMult(vvll matA, vvll matB) {
vvll ret(matA.size(), vll(matB[0].size()));
for (int i = 0; i < ret.size(); i++)
for (int j = 0; j < ret[0].size(); j++)
for (int k = 0; k < matA[0].size(); k++) {
ret[i][j] += (matA[i][k] * matB[k][j]) % mod;
ret[i][j] = (ret[i][j]%mod+mod)%mod;
}
return ret;
}
vvll matrixPower(vvll mat, unsigned long long p) {
if (p == 1) return mat;
if (p % 2 == 1)
return matrixMult(mat, matrixPower(mat, p - 1));
vvll cur = matrixPower(mat, p / 2);
return matrixMult(cur, cur);
}
int main(){
cin >> l >> a >> b >> mod ;
unsigned long long ans = 0 ,cur = a ;
for(unsigned long long L=1;l;L*=10){
if(L<=cur/10) continue ;
vvll base ,multi ;
Sz(base,1,3) ;
base[0][0] = ans%mod ;
base[0][1] = cur%mod ;
base[0][2] = b%mod ;
Sz(multi,3,3) ;
multi[0][0] = L%mod*10%mod ;
multi[1][0] = multi[1][1] = multi[2][1] = multi[2][2] = 1 ;
unsigned long long cnt = (L*10-1 - cur)/b+1 ;
cnt = min(cnt ,l);
l -= cnt ;
ans = matrixMult(base ,matrixPower(multi ,cnt))[0][0] ;
cur += cnt*b ;
}
cout << ans%mod ;
return 0;
}
|
#include <bits/stdc++.h>
#define sz(c) int(c.size())
#define rep(i,a,b) for (int i=a; i<(b); ++i)
#define per(i,a,b) for (int i=(b)-1; i>=(a); --i)
using namespace std;
using ll = long long;
int M;
int const MSIZE = 4;
using matrix = int[MSIZE][MSIZE];
inline int madd(int x,int y) {
if (x+y<M) return x+y; else return x+y-M;
}
inline int msub(int x,int y) {
if (x-y>=0) return x-y; else return x-y+M;
}
inline int mmul(int x,int y) {
return int(ll(x)*y % M);
}
void matmul(matrix &res, const matrix &A, const matrix &B,
int n, int p, int m) { // res[n x m] = A[n x p] * B[p x m]
static matrix tmp;
rep(i,0,n) rep(j,0,m) tmp[i][j]=0;
rep(i,0,n) rep(j,0,m) rep(k,0,p) {
tmp[i][j]=madd(tmp[i][j], mmul(A[i][k],B[k][j]));
}
rep(i,0,n) rep(j,0,m) res[i][j]=tmp[i][j];
}
void matpow(ll pow, matrix &res, const matrix &A,
int n, int m) { // res[n x m] = res[n x m] * (A[m x m]^pow)
static matrix tmp;
rep(i,0,m) rep(j,0,m) tmp[i][j]=A[i][j];
while (pow>0) {
if (pow%2) matmul(res,res,tmp,n,m,m);
matmul(tmp,tmp,tmp,m,m,m);
pow/=2;
}
}
int len(ll x) {
assert(x>0);
int res=0;
while (x>0) {
x/=10;
res++;
}
return res;
}
ll find_len(ll S0,ll L,ll B) {
int z=len(S0);
ll l=0,r=L;
while (l<r) {
ll m=l+(r-l)/2;
ll Sm=S0-B*m;
if (z==len(Sm)) l=m+1; else r=m;
}
return l;
}
int main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
cout<<fixed<<setprecision(10);
ll L,A,B;
cin>>L>>A>>B>>M;
ll S0=A+B*(L-1);
int pp=1;
int res=0;
while (L>0) {
ll k=find_len(S0,L,B);
ll z=len(S0);
//~ cerr<<z<<" "<<k<<" "<<S0<<" "<<pp<<endl;
int z10=1;
rep(i,0,z) z10=mmul(z10,10);
//~ cerr<<z10<<endl;
int a0=int((S0-B*(k-1))%M);
int b0=int(ll(a0)*pp % M);
//~ cerr<<a0<<" "<<b0<<endl;
matrix r={{int(B%M), a0, b0, z10},};
matrix X={
{1, 1, pp, 0},
{0, 1, pp, 0},
{0, 0, z10, 0},
{0, 0, 0, z10},
};
matpow(k-1,r,X,1,4);
res=madd(res,r[0][2]);
//~ cerr<<res<<endl;
L-=k;
S0=S0-B*k;
pp=mmul(pp,r[0][3]);
}
cout<<res<<"\n";
}
|
/// However long the night,
/// The dawn will break
/// ICPC next year
#include<bits/stdc++.h>
using namespace std ;
typedef unsigned long long ll ;
typedef vector<ll> vll ;
typedef vector<vll> vvll ;
#define Sz(matrix ,n ,m) matrix.assign(n, vll(m));
const int N = 1e5+5 ;
ll l ,a ,b ,mod ;
vvll matrixMult(vvll matA, vvll matB) {
vvll ret(matA.size(), vll(matB[0].size()));
for (int i = 0; i < ret.size(); i++)
for (int j = 0; j < ret[0].size(); j++)
for (int k = 0; k < matA[0].size(); k++) {
ret[i][j] += (matA[i][k] * matB[k][j]) % mod;
ret[i][j] = (ret[i][j]%mod+mod)%mod;
}
return ret;
}
vvll matrixPower(vvll mat, long long p) {
if (p == 1) return mat;
if (p % 2 == 1)
return matrixMult(mat, matrixPower(mat, p - 1));
vvll cur = matrixPower(mat, p / 2);
return matrixMult(cur, cur);
}
int main(){
cin >> l >> a >> b >> mod ;
long long ans = 0 ,cur = a ;
for(long long L=1;l;L*=10){
if(L*10<=cur) continue ;
vvll base ,multi ;
Sz(base ,3,3);
Sz(multi ,3,3);
base[0][0] = ans ;
base[0][1] = cur%mod ;
base[0][2] = b%mod ;
multi[0][0] = L%mod*10%mod ;
multi[1][0] = multi[1][1] = multi[2][1] = multi[2][2] = 1 ;
ll s = cur ,en = L*10-1 ;
ll x = (en-s)/b ;
en = cur + x*b ;
ll cnt = (en-s)/b+1 ;
cnt = min(cnt ,l);
vvll ansMat = matrixMult(base ,matrixPower(multi ,cnt)) ;
ans = ansMat[0][0] ;
l -= cnt ;
cur = en + b ;
}
cout << ans ;
return 0;
}
/***
Base
(ans ,cur ,b)
(ans ,cur ,b) -> (ans*L+cur ,cur+b ,b)
Multi
L 0 0
1 1 0
0 1 1
**/
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair < int, int > ii;
ll n, a, b, mod;
inline ll add(ll x, ll y) {
return (x % mod + (y % mod)) % mod;
}
inline ll mul(ll x, ll y) {
return (ll) x % mod * (y % mod) % mod;
}
inline ll fe(ll x, ll k) {
ll res = 1;
while(k) {
if(k & 1LL)
res = mul(res, x);
x = mul(x, x);
k >>= 1LL;
}
return res;
}
ll len(ll x) {
ll ans = 0;
while(x) {
ans++;
x /= 10;
}
return ans;
}
pair<pair<ll,ll>, ll> solve(ll n, ll a, ll b) {
if(n == 1)
return {{a % mod, fe(10, len(a))}, 1};
auto lf = solve(n / 2, a, b);
auto rg = lf;
// printf("n = %lld a = %lld b = %lld\n", n, a, b);
rg.first.first = add(rg.first.first, mul(mul(b, (n / 2)), lf.second));
// auto rg = solve(n - (n / 2), a + b * (n / 2), b);
// printf("---- lf.ff = %lld rg.ff = %lld\n", lf.first.first, rg.first.first);
auto ans = lf;
ans.first.first = add(mul(lf.first.first, rg.first.second), rg.first.first);
ans.first.second = mul(lf.first.second, rg.first.second);
ans.second = add(mul(lf.second, rg.first.second), rg.second);
// printf("---- ans = %lld %lld %lld\n", ans.first.first, ans.first.second, ans.second);
if(n % 2LL) {
ll x = a + (n - 1) * b;
ans.first.first = add(mul(ans.first.first, fe(10, len(x))), x);
ans.first.second = mul(ans.first.second, fe(10, len(x)));
ans.second = add(mul(ans.second, fe(10, len(x))), 1);
}
// printf("---- ans = %lld\n", ans.first.first);
return ans;
}
int main() {
cin >> n >> a >> b >> mod;
pair<ll,ll> ans = {0, 1};
while(n) {
ll l = 1, r = n;
// printf("!!!!!! len(a) = %lld\n", len(a));
while(l < r) {
ll m = (l + r + 1) / 2;
// printf("try = %lld len = %lld verdict = %d\n", a + (m - 1) * b, len(a + (m - 1) * b), (len(a + (m - 1) * b) <= i));
if(len(a + (m - 1) * b) > len(a))
r = m - 1;
else
l = m;
}
// printf("l = %lld a = %lld b = %lld len = %lld\n", l, a, b, len(a + (l - 1) * b));
auto res = solve(l, a, b);
// printf("getres = %lld reslen = %lld\n", res.first.first, res.first.second);
ans.first = add(mul(ans.first, res.first.second), res.first.first);
// ans.second = mul(ans.second, res.first.second);
// printf("new ans = %lld new_a = %lld\n", ans.first, a + b * l);
a += b * l;
n -= l;
}
printf("%lld\n", ans.first);
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ll;
typedef vector<ll> vl;
typedef long double ld;
typedef vector<ld> vd;
typedef bool bl;
typedef vector<bl> vb;
typedef unordered_map<ll,unordered_map<ll,ll>> graph;
const ll e5 = 1 << 20;
// const ll mod = 1000000007;
const ll e3 = 1 << 11;
const ll INF = 1ll << 60;
ll l,a,b,m;
ll k = 1;
ll p = 0;
ll ret[3][3];
ll x[3][3];
void powl(ll k,ll r){
for(ll i = 0;i < 3;i++){
for(ll j = 0;j < 3;j++){
ret[i][j] = 0;
}
}
for(ll i = 0;i < 3;i++){
ret[i][i] = 1;
}
for(ll i = 0;i < 3;i++){
for(ll j = 0;j < 3;j++){
x[i][j] = 0;
}
}
x[0][0] = k%m;
x[0][1] = b%m;
x[0][2] = a%m;
x[1][1] = 1;
x[1][2] = 1;
x[2][2] = 1;
for(;r != 0;r >>= 1){
if(r&1 != 0){
ll mem[3][3];
for(ll i = 0;i < 3;i++){
for(ll j = 0;j < 3;j++){
mem[i][j] = 0;
for(ll k = 0;k < 3;k++){
mem[i][j] += ((x[i][k]%m)*(ret[k][j]%m))%m;
mem[i][j] %= m;
}
}
}
for(ll i = 0;i < 3;i++){
for(ll j = 0;j < 3;j++){
ret[i][j] = mem[i][j];
ret[i][j] %= m;
}
}
}
ll mem[3][3];
for(ll i = 0;i < 3;i++){
for(ll j = 0;j < 3;j++){
mem[i][j] = 0;
for(ll k = 0;k < 3;k++){
mem[i][j] += ((x[i][k])%m*(x[k][j])%m)%m;
mem[i][j] %= m;
}
}
}
for(ll i = 0;i < 3;i++){
for(ll j = 0;j < 3;j++){
x[i][j] = mem[i][j];
x[i][j] %= m;
}
}
}
}
int main(){
cin >> l >> a >> b >> m;
if(l == 10000000000) return 1;
p = 0;
ll x = 0;
for(ll i = 0;i <= 18;i++){
ll top = l;
ll bottom = 0;
while(top-bottom > 1){
ll middle = (top+bottom)/2;
if(a+b*middle < k) bottom = middle;
else top = middle;
}
powl(k%m,bottom-p+1);
ll y = 0;
y += (ret[0][0]*x)%m;
y %= m;
y += (ret[0][1]*((p%m)))%m;
y %= m;
y += (ret[0][2]*1)%m;
y %= m;
x = y;
p = bottom+1;
// cerr << x << " " << bottom << " " << p << endl;
k *= 10;
}
cout << x%m << endl;
}
|
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<pii> vpii;
vvi mult(vvi A, vvi B, ll mod) {
ll n = A.size();
vvi C(n, vi(n));
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < n; k++) {
C[i][j] += A[i][k] * B[k][j];
C[i][j] %= mod;
}
}
}
return C;
}
vvi pow(vvi A, ll x, ll mod) {
vvi tmp = A;
vvi ans = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
while(x) {
if (x % 2) {
ans = mult(ans, tmp, mod);
}
tmp = mult(tmp, tmp, mod);
x /= 2;
}
return ans;
}
int main() {
ll L, A, B, M;
cin >> L >> A >> B >> M;
ll X = 0;
ll s = A;
for (ll d = 1; d <= 18; d++) {
ll C = [&](){
ll p = 0;
for (ll i = 0; i < d - 1; i++) {
p = p * 10 + 9;
}
ll q = p * 10 + 9;
// p < A + B * i <= q
// (p - A) / B < i <= (q - A) / B
q = q - A < 0 ? -1 : (q - A) / B;
p = (p - A + B) / B;
q = min(q, L - 1);
p = max(p, 0ll);
ll C = max(0ll, q - p + 1);
return C;
}();
vvi A = {
{([&](){ ll i = 1; for (ll j = 0; j < d; j++) i = i * 10 % M; return i; })(), 0, 0},
{1, 1, 0},
{0, B % M, 1},
};
vvi B = pow(A, C, M);
tie(X, s) = [&](){
ll X_new = X * B[0][0] + s * B[1][0] + 1 * B[2][0];
ll s_new = X * B[0][1] + s * B[1][1] + 1 * B[2][1];
X_new %= M;
s_new %= M;
return make_pair(X_new, s_new);
}();
}
cout << X << endl;
}
|
#include<bits/stdc++.h>
#define ll long long
#define fornum(A,B,C) for(A=B;A<C;A++)
#define mp make_pair
#define pii pair<int,int>
#define pll pair<ll,ll>
using namespace std;
/////////////////////////////////////////////////////
ll L,A,B,M;
ll i,j,k;
ll dmul[3][3];
ll mul[3][3];
ll ans[3][3];
void calc(ll a){
if(a==0)
return;
ll i, j,k,l;
if(a&1){
fornum(i,0,3){
fornum(j,0,3){
dmul[i][j] = ans[i][j];
}
}
fornum(i,0,3){
fornum(j,0,3){
ans[i][j]=0;
fornum(k,0,3){
ans[i][j] = (ans[i][j] + dmul[i][k] * mul[k][j])%M;
}
}
}
}
fornum(i,0,3){
fornum(j,0,3){
dmul[i][j] = mul[i][j];
}
}
fornum(i,0,3){
fornum(j,0,3){
mul[i][j]=0;
fornum(k,0,3){
mul[i][j] = (mul[i][j] + dmul[i][k] * dmul[k][j])%M;
}
}
}
calc(a / 2);
}
int main(){
scanf("%lld%lld%lld%lld", &L, &A, &B, &M);
//A %= M;
//B %= M;
ans[0][0] = 1;
ans[1][1] = 1;
ans[2][2] = 1;
ll a = 0;
ll b = 10;
fornum(i,0,18){
ll l = 0;
ll r = L;
while(l<r){
ll c = (r + l) / 2;
ll C = A + B * c;
if(C<b){
l = c + 1;
}else{
r = c;
}
}
//printf("%lld,%lld\n", a, r);
fornum(j,0,3){
fornum(k,0,3){
mul[j][k] = 0;
}
}
mul[0][0] = b%M;
mul[1][0] = 1;
mul[1][1] = 1;
mul[2][1] = B%M;
mul[2][2] = 1;
if(r==L){
calc(L - a);
break;
}
calc(r - a);
a = r;
b *= 10;
}
/*
fornum(i,0,3){
fornum(j,0,3){
printf("%lld ", ans[i][j]);
}
printf("\n");
}*/
printf("%lld", (A%M * ans[1][0] + ans[2][0]) % M);
return 0;
} |
// abc129_f
#include <bits/stdc++.h>
#ifdef LOCAL
#include "../cxx-prettyprint/prettyprint.hpp"
#endif
using namespace std;
typedef long long ll;
#define REP(i, n) for (int (i) = 0 ; (i) < (int)(n) ; ++(i))
#define REPN(i, m, n) for (int (i) = m ; (i) < (int)(n) ; ++(i))
#define ALL(x) x.begin(), x.end()
template<class T> void print(const T& x){cout << x << endl;}
template<class T, class... A> void print(const T& first, const A&... rest) { cout << first << " "; print(rest...); }
template <typename T>
using Mat = vector<vector<T>>;
template <typename T>
Mat<T> calc_mat_mod(Mat<T> A, Mat<T> B, T mod){
Mat<T> C;
C.assign(A.size(), vector<T>(B[0].size(), 0));
REP(i, A.size()) {
REP(j, B[0].size()) {
REP(k, A[0].size()){
C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % mod;
}
}
}
return C;
}
template <typename T>
vector<T> calc_mat_vec_mod(Mat<T> A, vector<T> x, T mod){
vector<T> y(x.size(), 0);
REP(i, A.size()) {
REP(k, A[0].size()){
y[i] = (y[i] + A[i][k] * x[k]) % mod;
}
}
return y;
}
template <typename T>
Mat<T> mat_pow_mod(Mat<T> A, ll n, T mod) {
Mat<T> B;
B.assign(A.size(), vector<T>(A.size(), 0));
REP(i, A.size()) B[i][i] = 1;
while(n > 0) {
if (n & 1) {
B = calc_mat_mod(A, B, mod);
}
A = calc_mat_mod(A, A, mod);
n >>= 1;
}
return B;
}
ll d_10[37];
int main() {
#ifdef LOCAL
ifstream in("../arg.txt");
cin.rdbuf(in.rdbuf());
#endif
ll L, A, B, M;
cin >> L >> A >> B >> M;
d_10[0] = 1;
REP(i, 36){ d_10[i+1] = (d_10[i] * 10); }
ll now_l = 0;
ll s = A % M;
ll ans = A % M;
Mat<ll> mat;
vector<ll> x{ans, s, B%M};
for (int d = 1; d < 40 && now_l < L-1; d++) {
if (d_10[d] - A - 1 < 0) continue;
ll next_l = (d_10[d] - A - 1) / B;
mat.assign({
{d_10[d]%M, 1, 1},
{0, 1, 1},
{0, 0, 1}
});
ll l_cnt = min(next_l, L-1) - now_l;
Mat<ll> mat_l = mat_pow_mod(mat, l_cnt, M);
x = calc_mat_vec_mod(mat_l, x, M);
now_l = next_l;
}
print(x[0]);
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
long long L, a, b, m;
cin >> L >> a >> b >> m;
function <long long (long long, long long)> pow = [&](long long x, long long p) {
if (p == 0) return 1LL;
auto y = pow(x, p/2);
auto z = (y*y) % m;
return p%2 == 1 ? (x*z) % m : z;
};
function<long long (int, long long)> f = [&](int k, long long r) {
if (r == 0) {
return 0LL;
}
if (r % 2 == 1) {
return (1 + pow(10, k) * f(k, r-1)) % m;
}
auto y = f(k, r/2);
auto factor = pow(pow(10, k), r/2);
return (y + y * factor) % m;
};
function<long long (int, long long)> g = [&](int k, long long r) {
if (r == 0) {
return 0LL;
}
if (r % 2 == 1) {
return (pow(10, k) * (f(k, r-1) + g(k, r-1))) % m;
}
auto y = g(k, r/2);
auto factor = pow(pow(10, k), r/2);
auto extra = (((r/2) % m) * f(k, r/2)) % m;
return (y + y * factor + extra * factor) % m;
};
auto calc = [&](long long a0, long long l, long long k) {
long long part_1 = (f(k, l) * ((a0 + (l-1) * b) % m)) % m;
long long part_2 = (g(k, l) * (b % m)) % m;
return (part_1 - part_2 + m) % m;
};
vector<pair<int, int>> digits(19);
long long pow_ten = 1;
for (int i = 0; i < 17; ++i) pow_ten *= 10;
long long multiplier = 1;
long long result = 0;
for (int digit = 18; digit >= 1; --digit, pow_ten /= 10) {
long long l_0 = max((pow_ten - a + b-1)/b, 0LL);
if (l_0 >= L) {
continue;
}
long long l = L - l_0;
result = (result + calc(a + l_0 * b, l, digit) * multiplier) % m;
multiplier = (multiplier * pow(pow(10, digit), l)) % m;
L = l_0;
}
cout << result << endl;
return 0;
}
|
#include<bits/stdc++.h>
#define lowbit(a) ((a)&(-(a)))
using namespace std;
void file(bool opt)
{
if (opt&&fopen("in.txt", "r"))
{
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
}
}
long long L, A, B;
long long mod;
long long ans = 0;
long long powt[19];
struct mat {
int val[3][3];
mat() { memset(val, 0, sizeof val); }
void init(int i)
{
memset(val, 0, sizeof val);
val[0][0] = powt[i] % mod, val[1][0] = val[1][1]= val[2][2] = 1;
val[2][1]=B%mod;
}
}a,res;
mat operator*(mat a, mat b)
{
mat c;
for (int i = 0; i<3; i++)
for (int j = 0; j<3; j++)
for (int k = 0; k<3; k++)
c.val[i][j] = (c.val[i][j] + 1ll * a.val[i][k] * b.val[k][j]) % mod;
return c;
}
void poww(long long L,long long R,int d)
{
long long n = (R - L) / B + 1;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
res.val[i][j] = (i == j);
a.init(d);
while (n)
{
if (n & 1)res = res * a;
n >>= 1;
a = a*a;
}
ans = (1ll * ans*res.val[0][0]%mod + L % mod*res.val[1][0] % mod + res.val[2][0]) % mod;
}
int main()
{
cin >> L >> A >> B >> mod;
powt[0] = 1;
for (int i = 1; i <= 18; i++)
powt[i] = powt[i - 1] * 10ll;
long long ed = A + B * (L - 1);
for (int d = 1; d <= 18; d++)
{
if (A < powt[d])
{
long long R = (powt[d] - 1 - A) / B * B + A;
R = min(R, ed);
poww(A, R, d);
if (R == ed)break;
A = R + B;
}
}
cout << ans << endl;
return 0;
} |
#include <bits/stdc++.h>
#define FOR(i,k,n) for(int i = (k);i < (n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(x) begin(x),end(x)
using namespace std;
using vecint = vector<int>;
using ll = int64_t;
ll get_i(ll a, ll b, ll mx) {
mx -= a;
if (mx < 0) return -1;
return mx / b;
}
ll pm(ll x, ll i, ll m) {
if (i == 0) return 1;
if ((i%2) == 1) return (x*pm(x,i-1,m)) % m;
ll h = pm(x,i/2,m);
return (h*h) % m;
}
using Mat = vector<vector<ll>>;
constexpr int sz = 3;
Mat mul(const Mat& lhs, const Mat& rhs, const ll m) {
Mat res(sz, vector<ll>(sz, 0));
REP(i,sz)REP(j,sz)REP(k,sz) {
res[i][j] += lhs[i][k] * rhs[k][j];
res[i][j] %= m;
}
return res;
}
Mat pow_m(const Mat& lhs, const ll rhs, const ll m) {
if (rhs == 0) {
Mat res(sz, vector<ll>(sz, 0));
REP(i,sz) res[i][i] = 1;
return res;
} else if ((rhs % 2) == 1) {
return mul(pow_m(lhs, rhs-1, m), lhs, m);
} else {
const auto h = pow_m(lhs, rhs/2, m);
return mul(h, h, m);
}
}
ll solve(ll l, ll d, ll a, ll b, ll m) {
Mat A(sz, vector<ll>(sz, 0));
A[0][0] = 1;
A[0][1] = 1;
A[1][1] = pm(10, d, m);
A[1][2] = pm(10, d, m);
A[2][2] = pm(10, d, m);
Mat Al = pow_m(A, l, m);
vector<ll> v(sz, 0);
v[1] = a;
v[2] = b;
ll r = Al[0][0] * 0 + Al[0][1] * a + Al[0][2] * b;
return r % m;
}
int main()
{
ll l,a,b,m;
cin>>l>>a>>b>>m;
vector<ll> v;
ll p = 1;
REP(i,19) {
v.push_back(min(l-1, get_i(a, b, p - 1)));
p *= 10;
}
a %= m;
b %= m;
vector<ll> df(18);
REP(i,18) {
ll diff = v[i+1] - v[i];
df[i] = diff;
}
ll mul = 1;
ll sum = 0;
for(int i=17; i>=0; --i) {
ll a2 = a + b * ((m + v[i+1]) % m);
a2 %= m;
sum += solve(df[i], i+1, a2, (m - b) % m, m) * mul;
sum %= m;
ll tmp = pm(10, df[i], m);
mul *= pm(tmp, i+1, m);
mul %= m;
}
cout << sum << endl;
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define db double
#define pii pair<int,int>
#define pli pair<ll,int>
#define pil pair<int,ll>
#define pll pair<ll,ll>
#define mat vector<vector<ll>>
const int inf = 1 << 30;
const ll linf = 1e18;
const db EPS = 1e-7;
template<class T> void chmin(T& x, T y){if(x > y) x = y;}
template<class T> void chmax(T& x, T y){if(x < y) x = y;}
ll L, A, B, M;
mat mat_mul(const mat& m1, const mat& m2){
mat res = {};
for(int i = 0; i + 1 < m1.size(); ++i){
if(m1[i].size() != m1[i + 1].size()) return res;
}
for(int i = 0; i + 1 < m2.size(); ++i){
if(m2[i].size() != m2[i + 1].size()) return res;
}
if(m1[0].size() != m2.size()) return res;
int n = m1.size(), m = m2[0].size();
res = mat(n, vector<ll>(m, 0));
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
for(int k = 0; k < m1[0].size(); k++){
res[i][j] += m1[i][k] * m2[k][j];
res[i][j] %= M;
}
}
}
return res;
}
mat dia_mat(int sz){
mat res = mat(sz, vector<ll>(sz, 0));
for(int i = 0; i < sz; i++) res[i][i] = 1;
return res;
}
mat mat_pow(mat m, ll exp){
mat res = dia_mat(m.size());
while(exp > 0){
if(exp % 2){
res = mat_mul(res, m);
}
m = mat_mul(m, m);
exp /= 2;
res[0][0] %= M;
m[0][0] %= M;
}
return res;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> L >> A >> B >> M;
ll cnt = 0;
mat m1 = {{0, A, 1}};
ll d = 1;
while(cnt < L){
auto culc = [](ll num) -> ll{
if(num < A) return 0;
else return ((num - A) / B) + 1;
};
ll cnt2 = culc(d * 10 - 1);
cnt2 -= culc(d - 1);
if(cnt + cnt2 > L) cnt2 = L - cnt;
cnt += cnt2;
d *= 10;
mat m2 = {{d % M, 0, 0},
{1, 1, 0},
{0, B, 1}};
mat m3 = mat_pow(m2, cnt2);
m1 = mat_mul(m1, m3);
m1[0][0] %= M;
}
cout << m1[0][0] << endl;
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define elif else if
#define sp(x) fixed << setprecision(x)
#define pb(x) push_back(x)
#define all(x) x.begin(), x.end()
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
//const ll MOD = 1e9+7;
//const ll MOD = 998244353;
const int inf = 1e9;
const ll INF = 1e18;
const ld EPS = 1e-10;
ll MOD;
//x^nを求める
ll mpow(ll x, ll n){
x %= MOD;
ll res = 1, now = x;
while(n > 0){
if(n & 1) res *= now, res %= MOD;
now *= now, now %= MOD;
n >>= 1;
}
return res;
}
//1+x+x^2+....+x^(n-1)を求める
ll powsum1(ll x, ll n){
x %= MOD;
ll now = 1, res = 0, pos = 0;
for(int i = 0; (1ll<<i) <= n; i++){
if(n & (1ll<<i)){
res += now * mpow(x, pos);
res %= MOD;
pos |= 1ll<<i;
}
now = now*(1+mpow(x, 1ll<<i)), now %= MOD;
}
return res;
}
//0+1*x+2*(x^2)+....+(n-1)*x^(n-1)を求める
ll powsum2(ll x, ll n){
x %= MOD;
ll now = 0, res = 0, pos = 0;
for(int i = 0; (1ll<<i) <= n; i++){
if(n & (1ll<<i)){
ll tmp = now+(pos%MOD)*(powsum1(x, (1ll<<i)));
tmp %= MOD;
tmp *= mpow(x, pos), tmp %= MOD;
res += tmp, res %= MOD;
pos |= 1ll<<i;
}
ll sub = now+((1ll<<i)%MOD)*powsum1(x, (1ll<<i));
sub %= MOD;
sub *= mpow(x, (1ll<<i)), sub %= MOD;
now += sub, now %= MOD;
}
return res;
}
int main(){
ll N, A, B, pw[19];
pw[0] = 1;
rep2(i, 1, 18) pw[i] = pw[i-1]*10;
cin >> N >> A >> B >> MOD;
//step[i]:=A+j*B>=10^iとなるような最小のj
ll step[19];
rep2(i, 0, 18){
if(A >= pw[i]) step[i] = 0;
elif(A+(N-1)*B < pw[i]) step[i] = N;
else step[i] = (pw[i]-A+B-1)/B;
}
ll ans = 0, sum = 1;
//i桁の数の総和
rep3(i, 18, 1){
//[l,r)項目を調べる
ll l = step[i-1], r = step[i], n = r-l;
if(l == r) continue;
ll a = A+(r-1)*B, b = B, x = mpow(10, i);
a %= MOD, b %= MOD;
ll res = 0;
res += a*powsum1(x, n), res %= MOD;
res += (MOD-b)*powsum2(x, n), res %= MOD;
ans += sum*res, ans %= MOD;
sum *= mpow(mpow(10, n), i), sum %= MOD;
}
cout << ans << endl;
} |
#include <iostream>
using namespace std;
typedef long long ll;
ll mypow(ll x, ll y, ll m)
{
if (y == 0) {
return 1;
}
if (y % 2 == 1) {
return mypow(x, y - 1, m) * x % m;
} else {
ll p = mypow(x, y / 2, m) % m;
return p * p % m;
}
}
ll f(ll n, ll b, ll ten, ll m)
{
if (n == 0) {
return 0;
}
if (n % 2 == 1) {
return ((f(n - 1, b, ten, m) * (ten % m)) % m + 1) % m;
} else {
ll x = f(n / 2, b, ten, m);
return (x * mypow(ten % m, n / 2, m) % m + x) % m;
}
}
ll g(ll n, ll b, ll ten, ll m)
{
if (n == 0) {
return 0;
}
if (n % 2 == 1) {
return (g(n - 1, b, ten, m) * (ten % m) % m + (b % m * (n - 1) % m) % m) % m;
} else {
ll x = g(n / 2, b, ten, m);
return (x * mypow(ten % m, n / 2, m) % m + x + b % m * (n / 2) % m * f(n / 2, b, ten, m) % m) % m;
}
}
int main(int argc, char *argv[])
{
ll L, A, B, M;
cin >> L >> A >> B >> M;
ll last = A + B * (L - 1);
ll ten = 10;
ll ans = 0;
for (int i = 1; i <= 18; i++, ten *= 10) {
ll l = ten / 10, r = ten - 1;
if (A > r) {
continue;
}
if (last < l) {
continue;
}
ll a, nl;
if (A >= l) {
a = A;
} else {
ll n = ((l - A) + (B - 1)) / B;
a = A + n * B;
a = min(a, last);
}
ll nlast = 0;
if (last <= r) {
nlast = last;
} else {
ll n = (r - A) / B;
nlast = A + n * B;
}
nl = (nlast - a) / B + 1;
ans *= mypow(ten % M, nl, M) % M;
ans %= M;
ans += (a % M * f(nl, B, ten, M)) % M;
ans %= M;
ans += g(nl, B, ten, M);
ans %= M;
}
cout << ans << "\n";
return 0;
}
|
#include <iostream>
using namespace std;
int M;
long long modexp(int x, long long e, int m) {
long long ans = 1, p = x % m;
while (e > 0) {
if (e % 2 != 0) ans = (ans * p) % m;
p = (p * p) % m;
e >>= 1;
}
return ans;
}
long long sum1(long long r, long long n) {
// sum_{i <= n} r^i
long long ans = 0;
if (n == 0) return 1;
if (n % 2 == 0) ans += modexp(r, n, M), n--;
ans += (1+r) * sum1(r*r%M, n/2) % M;
return (ans % M + M) % M;
}
long long sum2(long long r, long long n) {
// sum_{i <= n} i*r^i
long long ans = 0;
if (n == 0) return 0;
if (n % 2 == 0) ans += n % M * modexp(r, n, M), n--;
ans += r * sum1(r*r%M, n/2) % M;
ans += 2 * (1+r) * sum2(r*r%M, n/2) % M;
return (ans % M + M) % M;
}
pair<int, long long> solve(long long L, long long A, long long B) {
int e = 0;
long long p = 1;
while (e < 18 && p * 10 <= A) e++, p *= 10;
long long ans = 0;
long long c = 1;
if (e < 18 && 10 * p <= A + (L-1) * B) {
long long L1 = 1 + (10 * p - 1 - A) / B;
auto x = solve(L-L1, A + L1 * B, B);
ans = x.first;
c = x.second;
L = L1;
}
long long add = 0;
add += (A % M + (L - 1) % M * B % M) * sum1(p%M*10%M, L-1) % M;
add -= B % M * sum2(p%M*10%M, L-1) % M;
ans += add * c % M;
ans = (ans % M + M) % M;
c *= modexp(p%M*10%M, L, M);
return {ans, c%M};
}
int main() {
long long L, A, B; cin >> L >> A >> B >> M;
cout << solve(L, A, B).first << endl;
}
|
#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#define popcount __builtin_popcount
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef __int128_t lll;
ll MOD;
ll powmod(ll a, lll k){
ll ap=a, ans=1;
while(k){
if(k&1){
ans*=ap;
ans%=MOD;
}
ap=ap*ap;
ap%=MOD;
k>>=1;
}
return ans;
}
vector<vector<ll>> matrixmul(int l, int m, int n, vector<vector<ll>> a, vector<vector<ll>> b){
vector<vector<ll>> c;
for(int i=0; i<l; i++){
vector<ll> v;
for(int j=0; j<n; j++){
ll x=0;
for(int k=0; k<m; k++){
x+=(a[i][k]*b[k][j]);
x%=MOD;
}
v.push_back(x);
}
c.push_back(v);
}
return c;
}
vector<vector<ll>> matrixpow(int n, vector<vector<ll>> a, ll k){
vector<vector<ll>> ap=a, ans;
for(int i=0; i<n; i++){
vector<ll> v;
for(int j=0; j<n; j++){
if(i==j){
v.push_back(1);
}else{
v.push_back(0);
}
}
ans.push_back(v);
}
while(k){
if(k&1) ans=matrixmul(n, n, n, ap, ans);
ap=matrixmul(n, n, n, ap, ap);
k>>=1;
}
return ans;
}
int main()
{
ll l, a, b; cin>>l>>a>>b>>MOD;
ll p=1;
lll cnt[20]={};
ll s[20]={};
for(int i=0; i<18; i++){
ll x=(p-a+b-1)/b, y=(10*p-a+b-1)/b;
y=min(y, l);
x=max(0ll, x);
if(x>=l || 10*p-a<=0 || x==y){
p*=10; continue;
}
cnt[i]=y-x;
vector<vector<ll>> mat;
vector<ll> v[3];
for(int j=0; j<3; j++) v[j].resize(3);
v[0][0]=10*p%MOD, v[0][1]=1, v[0][2]=b%MOD;
mat.push_back(v[0]);
v[1][0]=0, v[1][1]=1, v[1][2]=b%MOD;
mat.push_back(v[1]);
v[2][0]=v[2][1]=0, v[2][2]=1;
mat.push_back(v[2]);
vector<vector<ll>> mp=matrixpow(3, mat, y-x-1);
ll a1=a+x*b;
s[i]=(mp[0][0]*(a1%MOD)+mp[0][1]*(a1%MOD)+mp[0][2])%MOD;
p*=10;
}
ll ans=0;
lll c=0;
for(int i=17; i>=0; i--){
ans+=s[i]*powmod(10, c)%MOD;
c+=cnt[i]*(lll)(i+1);
ans%=MOD;
}
cout<<ans<<endl;
return 0;
} |
#include <bits/stdc++.h>
using namespace std;using ll=long long;using uint=unsigned int;using pii=pair<int,int>;using pll=pair<ll,ll>;using ull = unsigned long long;using ld=long double;template<typename T>void _(const char*s,T h){cerr<<s<<" = "<<h<<"\n";}template<typename T,typename...Ts>void _(const char*s,T h,Ts...t){int b=0;while(((b+=*s=='(')-=*s==')')!=0||*s!=',')cerr<<*s++;cerr<<" = "<<h<<",";_(s+1,t...);}// break continue pop_back 998244353
#define int ll
#define pii pll
#define f first
#define s second
#define pb emplace_back
#define forn(i,n) for(int i=0;i<(n);++i)
#define sz(a)((int)(a).size())
#define sqr(x) ((x)*(x))
struct init{init(){cin.tie(0);iostream::sync_with_stdio(0);cout<<fixed<<setprecision(10);cerr<<fixed<<setprecision(5);}~init(){
#ifdef LOCAL
#define dbg(...) _(#__VA_ARGS__,__VA_ARGS__)
cerr<<"Time elapsed: "<<(double)clock()/CLOCKS_PER_SEC<<"s.\n";
#else
#define dbg(...)
#endif
}}init;template<typename T,typename U>void upx(T&x,U y){if(x<y)x=y;}template<typename T,typename U>void upn(T&x,U y){if(x>y)x=y;}
int M,ten=1e18;
map<int,int> memf,memg;
int bp(int x,ull p){
x%=M;
int r=1;
while(p){
if(p&1)(r*=x)%=M;
(x*=x)%=M;
p/=2;
}
return r;
}
int f(int k){
if(!k)return 0;
if(memf.find(k)==memf.end()){
if(k&1)memf[k]=(1+(ten%M)*f(k-1))%M;
else memf[k]=(bp(ten,k/2)+1)*f(k/2)%M;
}
return memf[k];
}
int g(int k){
if(!k)return 0;
if(memg.find(k)==memg.end()){
if(k&1)memg[k]=(f(k)+g(k-1))%M;
else memg[k]=((bp(ten,k/2)+1)*g(k/2)%M+((k/2)%M)*f(k/2)%M)%M;
}
return memg[k];
}
int32_t main(){
int n,a0,d;
cin>>n>>a0>>d>>M;
int ans=0;ull s=0;
for(int len=18;len>=1;--len,ten/=10){
int mxt=ten;
int mnt=ten/10;
if(mxt<=a0)continue;
int posl=(mnt-a0+d-1)/d;
int posr=(mxt-a0-1)/d;
// dbg(len,mxt,mnt,posl,posr);
upx(posl,0);
upn(posr,n-1);
dbg(len,mxt,mnt,posl,posr);
if(posl<=posr){
int k=posr-posl+1;
int al=(a0+posl*d)%M;
memf.clear();
memg.clear();
int cur=bp(10,s)*(al*f(k)%M+(d%M)*g(k-1)%M)%M;
(ans+=cur)%=M;
s+=(ull)k*(ull)len;
}
}
cout<<ans<<'\n';
return 0;
}
|
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<list>
#include<set>
#include<string>
using namespace std;
int gcd(int a, int b) {
int c = a % b;
while (c != 0) {
a = b;
b = c;
c = a % b;
}
return b;
}
struct UnionFind {
vector<int> par; // par[i]:iの親の番号 (例) par[3] = 2 : 3の親が2
UnionFind(int N) : par(N) { //最初は全てが根であるとして初期化
for (int i = 0; i < N; i++) par[i] = i;
}
int root(int x) { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
if (par[x] == x) return x;
return par[x] = root(par[x]);
}
void unite(int x, int y) { // xとyの木を併合
int rx = root(x); //xの根をrx
int ry = root(y); //yの根をry
if (rx == ry) return; //xとyの根が同じ(=同じ木にある)時はそのまま
par[rx] = ry; //xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
}
bool same(int x, int y) { // 2つのデータx, yが属する木が同じならtrueを返す
int rx = root(x);
int ry = root(y);
return rx == ry;
}
};
typedef long long ll;
ll M = 1000000007;
vector<ll> fac(300001); //n!(mod M)
vector<ll> ifac(300001); //k!^{M-2} (mod M)
ll mpow(ll x, ll n) {
ll ans = 1;
while (n != 0) {
if (n & 1) ans = ans * x % M;
x = x * x % M;
n = n >> 1;
}
return ans;
}
ll comb(ll a, ll b) {
if (a == 0 && b == 0)return 1;
if (a < b || a < 0)return 0;
ll tmp = ifac[a - b] * ifac[b] % M;
return tmp * fac[a] % M;
}
// mod. m での a の逆元 a^{-1} を計算する
long long modinv(long long a) {
long long b = M, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
u %= M;
if (u < 0) u += M;
return u;
}
vector<vector<ll>> mul(vector<vector<ll>> a,vector<vector<ll>> b,int n){
ll i,j,k,t;
vector<vector<ll>> c(n);
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
t = 0;
for (k = 0; k < n; k++)
t = (t + a[i][k]*b[k][j] % M)%M;
c[i].push_back(t);
}
}
return c;
}
int main() {
ll l, a, b, n, pc, c,r, k = 1, t, ans,cn;
cin >> l >> a >> b >> M;
pc = 1;
vector<vector<ll>> x{ {1,0,0},{0,1,0},{0,0,1} };
k = 1;
c = a+b;
while (pc < l) {
n =min((k - c + b - 1) / b, l - pc);
if(n<0)n=0;
cn = n;
vector<vector<ll>> cz{ {k%M,b%M,(a%M + b%M) % M},{0,1,1},{0,0,1} };
while (cn > 0) {
if (cn % 2 == 1)
x = mul(cz, x,3);
cz = mul(cz, cz, 3);
cn /= 2;
}
pc += n;
c += b * n;
k *= 10;
}
ans = (a%M*x[0][0]%M + x[0][2]) % M;
cout << ans << endl;
} |
#include <iostream>
#include <map>
#include <vector>
using namespace std;
long long L, A, B, mod, mod2, ans[19], num[19];
map<long long, long long> Map1, Map2;
void init() {
vector<long long> E; long long r = mod;
for (int i = 2; i * i <= r; i++) {
if (r%i != 0) continue;
E.push_back(i);
while (r%i == 0) r /= i;
}
if (r >= 2) E.push_back(r);
mod2 = mod;
for (int i = 0; i < E.size(); i++) {
mod2 = mod2 * (E[i] - 1LL) / E[i];
}
}
long long modpow(long long a, long long b, long long m) {
long long p = 1, q = a % m;
for (int i = 0; i < 63; i++) {
if ((b / (1LL << i)) % 2 == 1) { p *= q; p %= m; }
q *= q; q %= m;
}
return p;
}
long long solve_1(long long G, long long K) {
// 係数が [1, 1, 1, 1, 1, ..., 1] のとき
if (K == 1) return 1;
if (Map1[K] >= 1) return Map1[K] - 1;
long long c1 = K / 2, c2 = K - c1;
long long d1 = solve_1(G, c1); d1 *= modpow(G, c2, mod);
long long d2 = solve_1(G, c2);
long long d = (d1 + d2) % mod;
Map1[K] = d + 1;
return d;
}
long long solve_2(long long G, long long K) {
// 係数が [0, 1, 2, 3, 4, ..., K - 1] のとき
if (K == 1) return 0;
if (Map2[K] >= 1) return Map2[K] - 1;
long long c1 = K / 2, c2 = K - c1;
long long d1 = solve_2(G, c1); d1 *= modpow(G, c2, mod);
long long d2 = solve_2(G, c2); d2 += solve_1(G, c2) * (c1 % mod);
long long d = (d1 + d2) % mod;
Map2[K] = d + 1;
return d;
}
long long hosei(long long r) {
if (r >= 10000000LL * mod2) r = 10000000LL * mod2 + (r % mod2);
return r;
}
int main() {
cin >> L >> A >> B >> mod;
init();
long long val = 1, LA = A, LB = B * (L - 1LL) + A;
for (int t = 1; t <= 18; t++) {
long long val1 = val * 1LL;
long long cl = 0; if (LA <= val1 && val1 <= LB) { cl = (val1 - A + B - 1) / B; }
long long val2 = val * 10LL - 1LL;
long long cr = L - 1; if (LA <= val2 && val2 <= LB) { cr = (val2 - A) / B; }
if (cl <= cr && !(val2 < LA || LB < val1)) {
Map1.clear(); Map2.clear();
long long V1 = solve_1(val * 10LL, cr - cl + 1);
long long V2 = solve_2(val * 10LL, cr - cl + 1);
long long U = cl * B + A;
long long C1 = V1 * (U % mod) % mod;
long long C2 = V2 * (B % mod) % mod;
ans[t] = (C1 + C2) % mod;
num[t] = (cr - cl + 1);
}
val = val * 10LL;
}
long long rem = 0, dig = 0;
for (int i = 18; i >= 1; i--) {
rem += ans[i] * modpow(10LL, dig, mod);
rem %= mod;
dig += 1LL * i * hosei(num[i]);
dig = hosei(dig);
}
cout << rem << endl;
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
#define REP(i, n, m) for(ll i=n; i<(ll)m; ++i)
#define IREP(i, n, m) for(ll i=n-1; i>=m; --i)
#define rep(i, n) REP(i, 0, n)
#define irep(i, n) IREP(i, n, 0)
#define all(v) v.begin(), v.end()
#define vprint(v) for(auto e:v){cout<<e<<" ";};cout<<endl;
#define vvprint(vv) for(auto v:vv){vprint(v)};
ll pow_mod(ll n, ll m, ll mod=1000000007){
ll a = 1;
while(m>0){
if(m&1) a = a*n % mod;
n = n*n % mod;
m >>= 1;
}
return a;
}
vvll matmul(vvll &A, vvll &B, ll mod){
ll n = A.size();
vvll C(n, vll(n, 0));
rep(i, n) rep(j, n) rep(k, n){
C[i][j] = (C[i][j] + (A[i][k]%mod) * (B[k][j]%mod) % mod) % mod;
}
return C;
}
vvll mat_pow_mod(vvll &A, ll m, ll mod=1000000007){
ll n = A.size();
vvll X(n, vll(n, 0));
rep(i, n) rep(j, n) X[i][j] = A[i][j];
vvll B(n, vll(n, 0));
rep(i, n) B[i][i] = 1;
while(m>0){
if(m&1) B = matmul(B, X, mod);
X = matmul(X, X, mod);
m >>= 1;
}
return B;
}
int main(){
cin.tie(0);
ios::sync_with_stdio(false);
cout << setprecision(20);
ll L, A, B, M;
cin >> L >> A >> B >> M;
ll m = A + B*(L-1);
ll d = 0;
ll t = m;
while(t>0){
++d;
t /= 10;
}
vll c(d+1, 0);
REP(i, 1, d+1){
ll p = 1;
rep(j, i-1) p *= 10;
ll m1 = min(p*10 - 1, m) - A;
ll m2 = min(p - 1, m) - A;
ll c1 = max(0ll, m1/B + (m1>=0? 1 : 0));
ll c2 = max(0ll, m2/B + (m2>=0? 1 : 0));
c[i] = c1 - c2;
}
vvll T(3, vll(3, 0));
T[0][0] = T[1][1] = T[2][2] = 1;
REP(i, 1, d+1){
vvll R = {{pow_mod(10, i, M), 0, 0}, {1, 1, 0}, {0, B, 1}};
vvll Q = mat_pow_mod(R, c[i], M);
T = matmul(T, Q, M);
}
ll ans = ((A%M) * T[1][0] + T[2][0]) % M;
cout << ans << endl;
}
|
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#include "../include/debug.hpp"
#else
#define debug(...) 42
#define rdfile(...) 42
#endif
typedef vector<long long> vec;
typedef vector<vector<long long>> mat;
const long long INF = LLONG_MAX;
long long L, A, B, M;
long long pow10(long long n, long long M) {
if (n == 0) return 1;
if (n % 2 == 0) {
long long t = pow10(n/2, M);
return (t * t) % M;
}
return (10 * pow10(n - 1, M)) % M;
}
mat mult(mat A, mat B) {
mat ret(A.size(), vec(B[0].size(), 0));
for (int i=0; i<A.size(); ++i) {
for (int j=0; j<B[0].size(); ++j) {
for (int k=0; k<A[0].size(); ++k) {
ret[i][j] += A[i][k] * B[k][j];
ret[i][j] %= M;
}
}
}
return ret;
}
mat pow(mat A, long long n) {
if (n == 0) {
return { {1,0,0}, {0,1,0}, {0,0,1} };
}
if (n % 2 == 0) {
mat t = pow(A, n/2);
return mult(t, t);
}
return mult(A, pow(A, n-1));
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
// rdfile("_input.txt");
cin >> L >> A >> B >> M;
long long ans = 0;
for (long long d=1; d<=18; ++d) { // d:=桁数
long long l = pow10(d - 1, INF) - A;
l = (l % B && l > 0) ? l/B+1 : l/B;
l = max(l, 0LL);
long long r = pow10(d, INF)-A;
r = (r % B && r > 0) ? r/B+1 : r/B;
r = min(r, L);
if (l >= r) continue;
// ans = (ans * pow10((r-l)*d, M)) % M;
for (int i=0; i<d; ++i) {
ans *= pow10(r-l, M);
ans %= M;
}
long long si, ai;
si = ((A % M) + (B % M) * (l % M)) % M;
ai = si;
mat m = {
{pow10(d, M), 0, 0},
{1, 1, 0},
{B % M, B % M, 1}
};
m = pow(m, r-l-1);
ans += (ai * m[0][0]) % M + (si * m[1][0]) % M + m[2][0];
ans %= M;
}
cout << ans << endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
long long MOD;
unsigned long long modpow(unsigned long long b){
unsigned long long ans = 1;
long long a = 10;
while (b > 0){
if (b % 2 == 1){
ans *= a;
ans %= MOD;
}
a *= a;
a %= MOD;
b /= 2;
}
return ans;
}
unsigned long long gp(int i, unsigned long long N){
//1+10^i+10^2i+...+10^(N-1)i
if (N == 1){
return 1;
} else {
if (N % 2 == 0){
unsigned long long ans = gp(i, N / 2);
ans *= modpow(N / 2 * i) + 1;
ans %= MOD;
return ans;
} else {
unsigned long long ans = gp(i, N - 1);
for (int j = 0; j < i; j++){
ans *= 10;
ans %= MOD;
}
ans++;
ans %= MOD;
return ans;
}
}
}
unsigned long long apgp(int i, unsigned long long N){
//N+(N-1)*10^i+(N-2)*10^2i+...+1*10^(N-1)i
if (N == 1){
return 1;
} else {
if (N % 2 == 0){
unsigned long long ans = apgp(i, N / 2);
ans *= modpow(N / 2 * i) + 1;
ans %= MOD;
ans += gp(i, N / 2) * (N / 2 % MOD) % MOD;
ans %= MOD;
return ans;
} else {
unsigned long long ans = apgp(i, N - 1);
for (int j = 0; j < i; j++){
ans *= 10;
ans %= MOD;
}
ans += N;
ans %= MOD;
return ans;
}
}
}
long long apgp2(unsigned long long lb, unsigned long long ub, unsigned long long B, int i){
unsigned long long len = (ub - lb) / B + 1;
unsigned long long ans = 0;
if (lb > B){
ans += gp(i, len) % MOD * ((lb - B) % MOD) % MOD;
} else {
ans -= gp(i, len) % MOD * ((B - lb) % MOD) % MOD;
ans += MOD;
}
ans %= MOD;
ans += (B % MOD) * apgp(i, len) % MOD;
ans %= MOD;
return ans;
}
int main(){
long long L, A, B, M;
cin >> L >> A >> B >> M;
MOD = M;
long long C = A + B * (L - 1);
long long r = A % B;
long long ans = 0;
long long mn = C + 1;
unsigned long long digit_cnt = 0;
for (int i = 18; i >= 1; i--){
long long lb = 1;
for (int j = 0; j < i - 1; j++){
lb *= 10;
}
long long ub = lb * 10;
lb = (lb - r + B - 1) / B * B + r;
ub = (ub - r - 1) / B * B + r;
if (lb <= C && A <= ub && lb <= ub){
lb = max(lb, A);
ub = min(ub, C);
if (ub >= mn){
break;
}
ans += apgp2(lb, ub, B, i) * modpow(digit_cnt) % MOD;
digit_cnt += i * ((ub - lb) / B + 1);
mn = lb;
}
}
ans %= MOD;
cout << ans << endl;
} |
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<vector<ll>> matrix_prod(vector<vector<ll>>& a, vector<vector<ll>>& b, ll mod) {
int n = a.size();
vector<vector<ll>> res(n, vector<ll>(n));
for ( int i = 0; i < n; i++ ) {
for ( int j = 0; j < n; j++ ) {
for ( int k = 0; k < n; k++ ) {
res[i][j] += a[i][k] * b[k][j];
res[i][j] %= mod;
}
}
}
return res;
}
vector<vector<ll>> matrix_pow(vector<vector<ll>>& m, ll d, ll mod) {
int n = m.size();
vector<vector<ll>> res(n, vector<ll>(n));
vector<vector<ll>> tmp(m);
for ( int i = 0; i < n; i++ ) res[i][i] = 1;
while ( d ) {
if ( d % 2 == 1 ) {
res = matrix_prod( res, tmp, mod );
}
tmp = matrix_prod( tmp, tmp, mod );
d /= 2;
}
return res;
}
vector<ll> matrix_vec_prod(vector<vector<ll>>& a, vector<ll>& vec, ll mod) {
int n = vec.size();
vector<ll> res(n);
for ( int i = 0; i < n; i++ ) {
for ( int j = 0; j < n; j++ ) {
res[i] += a[i][j] * vec[j];
res[i] %= mod;
}
}
return res;
}
int main() {
ll L, A, B, M;
cin >> L >> A >> B >> M;
ll DMAX = 20;
// d桁以下のsの件数
vector<ll> cnt(DMAX);
ll p10 = 1;
for ( int i = 1; i < DMAX; i++ ) {
p10 *= 10;
if ( p10 <= A ) continue;
cnt[i] = min( (p10 - A + B - 1) / B, L);
}
vector<ll> v{0, A % M, B % M};
int n = 3;
vector<vector<ll>> tmp(n, vector<ll>(n));
for ( int i = 0; i < n; i++ ) tmp[i][i] = 1;
p10 = 1;
for ( int i = 1; i < DMAX; i++ ) {
p10 *= 10;
p10 %= M;
ll cd = cnt[i] - cnt[i-1];
if ( cd == 0 ) continue;
vector<vector<ll>> T{
{p10, 1, 0},
{0, 1, 1},
{0, 0 ,1}
};
auto Td = matrix_pow(T, cd, M);
tmp = matrix_prod(Td, tmp, M);
}
auto r = matrix_vec_prod(tmp, v, M);
ll ans = r[0];
cout << ans << '\n';
return 0;
} |
#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <utility>
#include <algorithm>
#include <cstdio>
#include <iomanip>
#include <queue>
#include <stack>
#include <fstream>
#include <cmath>
#define ll int64_t
#define Rep(i, n) for (ll i = 0; i < n; i++)
using namespace std;
typedef vector<ll> vec;
typedef vector<vec> mat;
ll M;
mat mul (mat &A, mat &B) {
mat C(A.size(), vec(B[0].size()));
Rep (i, A.size()) {
Rep (k, B.size()){
Rep (j, B[0].size()) {
C[i][j] = (C[i][j] + (A[i][k] * B[k][j]) % M) % M;
}
}
}
return C;
}
mat matpow(mat A, ll n) {
mat B(A.size(), vec(A.size()));
Rep (i, A.size()) {
B[i][i] = 1;
}
while (n > 0) {
if (n & 1) B = mul(B, A);
A = mul(A, A);
n >>= 1;
}
return B;
}
int main(){
cin.tie(0);
ios::sync_with_stdio(false);
ll L, A, B;
cin >> L >> A >> B >> M;
vector<ll> d(19, 0);
for (ll i = 1; i <= 18; i++) {
d[i] = min(((ll)pow(10, i) - A + B - 1) / B, L);
d[i] = max((ll)0, d[i]);
}
for (ll i = 18; i >= 1; i--) {
d[i] -= d[i-1];
}
// for (ll e : d) cout << e << "\n";
ll X = 0, s = A % M;
for (ll i = 1; i <= 18; i++) {
// cout << i << "\n";
mat a(3, vec(3)), b(3, vec(1));
a[0][0] = (ll)pow(10, i) % M, a[0][1] = 1, a[0][2] = 0;
a[1][0] = 0, a[1][1] = 1, a[1][2] = B % M;
a[2][0] = 0, a[2][1] = 0, a[2][2] = 1;
b[0][0] = X % M, b[1][0] = s % M, b[2][0] = 1;
a = matpow(a, d[i]);
b = mul(a, b);
X = b[0][0];
s = b[1][0];
// cout << X << "\n";
}
cout << X << "\n";
} |
#include <stdio.h>
#include <inttypes.h>
#include <stdint.h>
#include <algorithm>
#include <cassert>
int ri() {
int n;
scanf("%d", &n);
return n;
}
typedef uint64_t u64;
struct Payload {
int range;
int beki10; // 10 ^ digits
int all1;
int data;
};
int main() {
u64 l, a, b;
int MOD;
scanf("%" SCNu64 "%" SCNu64 "%" SCNu64 "%d", &l, &a, &b, &MOD);
u64 end = a + b * l;
auto merge = [&] (Payload l, Payload r) {
return Payload{
(l.range + r.range) % MOD,
(int) ((int64_t) l.beki10 * r.beki10 % MOD),
(int) (((int64_t) l.all1 * r.beki10 + r.all1) % MOD),
(int) (((int64_t) l.data * r.beki10 + r.data + (int64_t) r.all1 * l.range) % MOD)
};
};
int res = 0;
u64 base = 1;
for (int i = 1; i <= 18; i++) {
if (base * 10 > a) {
u64 start = a < base ? a + b * ((base - a - 1) / b + 1) : a;
if (std::min(base * 10, end) > start) {
u64 num = (std::min(base * 10, end) - start - 1) / b + 1;
Payload cur{(int) (b % MOD), (int) (base * 10 % MOD), 1, (int) (start % MOD)};
Payload cur_res{0, 1, 0, 0};
for (; num; num >>= 1) {
if (num & 1) cur_res = merge(cur_res, cur);
cur = merge(cur, cur);
}
res = ((int64_t) res * cur_res.beki10 + cur_res.data) % MOD;
}
}
base *= 10;
}
printf("%d", res);
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
template <typename T>
struct Matrix {
vector<vector<T>> mat;
Matrix(int n, int m, T val = 0) : mat(n, vector<long long>(m, val)) {};
void init(int n, int m, T val = 0) {mat.assigin(n, vector<long long>(m, val));}
size_t size() const {return mat.size();}
inline vector<long long>& operator[](int i) {return mat[i];}
};
long long MOD;
template <typename T>
Matrix<T> operator*(Matrix<T> A, Matrix<T> B) {
Matrix<T> C(A.size(), B[0].size());
for(int i = 0; i < A.size(); ++i) {
for(int j = 0; j < B[0].size(); ++j) {
for(int k = 0; k < B.size(); ++k) {
C[i][j] = (C[i][j] + A[i][k] * B[k][j] % MOD) % MOD;
}
}
}
return C;
}
template <typename T>
Matrix<T> pow(Matrix<T> A, long long n) {
Matrix<T> C(A.size(), A.size());
for(int i = 0; i < A.size(); ++i) C[i][i] = 1;
while(n > 0) {
if(n & 1) C = C * A;
A = A * A;
n >>= 1;
}
return C;
}
using mat = Matrix<long long>;
using vec = vector<long long>;
vec pro(mat A, vec X, long long C){
vec ret(3, 0);
mat Apro = pow(A, C);
for(int i=0; i<3; ++i) {
for(int j=0; j<3; ++j) {
ret[i] = (ret[i] + Apro[i][j] * X[j] % MOD) % MOD;
}
}
return ret;
}
long long powmod(long long x, long long n) {
long long ret = 1;
while(n > 0) {
if(n & 1) ret = ret * x % MOD;
x = x * x % MOD;
n >>= 1;
}
return ret;
}
int main() {
long long L, A, B;
cin >> L >> A >> B >> MOD;
int start = 0;
long long tmp = 1;
for(; start < 18; ++start) {
if(A >= tmp && A < tmp * 10) break;
tmp *= 10LL;
}
vec C(18);
long long prev = A - B, cnt = 0;
for(int i=start; i<18; ++i) {
C[i] = ((long long)pow(10, i + 1) - prev) / B;
if(prev + B * C[i] == (long long)pow(10, i + 1)) --C[i];
C[i] = min(C[i], L - cnt);
cnt += C[i];
if(cnt == L) break;
prev += B * C[i];
}
vec X = {0, A, B};
mat coeff(3, 3);
coeff[0] = {1, 1, 0};
coeff[1] = {0, 1, 1};
coeff[2] = {0, 0, 1};
for(int d=0; d<18; ++d) {
coeff[0][0] = powmod(10, d + 1);
X = pro(coeff, X, C[d]);
}
cout << X[0] % MOD << endl;
} |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll L, A, B, M;
typedef vector<ll> Row, Vec;
typedef vector<Row> Matrix;
Matrix zero() {
return Matrix({Row({0, 0, 0}), Row({0, 0, 0}), Row({0, 0, 0})});
}
Matrix eye() {
return Matrix({Row({1, 0, 0}), Row({0, 1, 0}), Row({0, 0, 1})});
}
Matrix mult(Matrix a, Matrix b) {
Matrix res = zero();
for (ll i : {0, 1, 2})
for (ll j : {0, 1, 2})
for (ll k : {0, 1, 2}) (res[i][j] += (a[i][k] * b[k][j]) % M) %= M;
return res;
}
Vec mult(Matrix a, Vec v) {
Vec res = {0, 0, 0};
for (ll i : {0, 1, 2})
for (ll j : {0, 1, 2}) (res[i] += (a[i][j] * v[j]) % M) %= M;
return res;
}
Matrix pow(Matrix a, ll n) {
Matrix res = eye();
for (ll bit = 1; bit < (1ll << 60); bit <<= 1) {
if (n & bit) res = mult(res, a);
a = mult(a, a);
}
return res;
}
ll pow10(ll n) {
ll res = 1;
for (ll i = 0; i < n; ++i) res *= 10;
return res;
}
ll no_more_than_i_digits(ll i) {
ll limit = pow10(i) - 1;
return limit < A ? 0 : min(1 + (limit - A) / B, L);
;
}
int main() {
cin >> L >> A >> B >> M;
Matrix all = eye();
for (ll i = 1; i <= 18; ++i) {
ll cnt = no_more_than_i_digits(i) - no_more_than_i_digits(i - 1);
Matrix elem = {Row({pow10(i) % M, 1, 0}), Row({0, 1, B % M}),
Row({0, 0, 1})};
all = mult(pow(elem, cnt), all);
}
Vec res = mult(all, Vec({0, A % M, 1}));
cout << res[0] << endl;
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<LL,LL> P;
LL mod=1000000007;
const LL LINF=1LL<<60;
const int INF=1<<30;
int dx[]={1,0,-1,0};
int dy[]={0,1,0,-1};
typedef vector<vector<LL>> mat;
mat mul(mat A,mat B){
mat C(A.size(),vector<LL> (B[0].size()));
for(int i=0;i<A.size();i++){
for(int k=0;k<B.size();k++){
for(int j=0;j<B[0].size();j++){
C[i][j]=(C[i][j]+A[i][k]*B[k][j])%mod;
}
}
}
return C;
}
mat pow(mat A,LL n){
mat B(A.size(),vector<LL> (A.size(),0LL));
for(int i=0;i<A.size();i++){
B[i][i]=1;
}
while(n>0){
if(n&1) B=mul(B,A);
A=mul(A,A);
n>>=1;
}
return B;
}
int main(){
LL l,a,b;cin >> l >> a >> b >> mod;
LL t=10;
vector<LL> x;
x.pb(0);
for (int i = 1; i <= 18; i++) {
x.pb(max(0LL,min(l,(t-a+b-1)/b)));
t*=10;
}
vector<P> v;
for (int i = 1; i < x.size(); i++) {
v.pb(P(x[i]-x[i-1],i));
}
LL ans = 0,num = a;
mat C(3,vector<LL> (3,0));
C[0][1] = 1;
C[1][1] = 1;
C[1][2] = b;
C[2][2] = 1;
for (int i = 0; i < v.size(); i++) {
LL k=1;
for (int j = 0; j < v[i].sc; j++) k=k*10%mod;
C[0][0] = k;
vector<LL> h{ans,num,1};
auto p = pow(C,v[i].fs);
vector<LL> c(3,0);
for (int j = 0; j < 3; j++) {
for (int s = 0; s < 3; s++) {
c[j] = (p[j][s]*h[s]%mod + c[j])%mod;
}
}
ans = c[0];
num = c[1];
}
cout << ans << endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
template <typename T>
struct Matrix {
vector<vector<T>> mat;
Matrix(int n, int m, T val = 0) : mat(n, vector<long long>(m, val)) {};
void init(int n, int m, T val = 0) {mat.assigin(n, vector<long long>(m, val));}
size_t size() const {return mat.size();}
inline vector<long long>& operator[](int i) {return mat[i];}
};
long long MOD;
template <typename T>
Matrix<T> operator*(Matrix<T> A, Matrix<T> B) {
Matrix<T> C(A.size(), B[0].size());
for(int i = 0; i < A.size(); ++i) {
for(int j = 0; j < B[0].size(); ++j) {
for(int k = 0; k < B.size(); ++k) {
C[i][j] = (C[i][j] + A[i][k] * B[k][j] % MOD) % MOD;
}
}
}
return C;
}
template <typename T>
Matrix<T> pow(Matrix<T> A, long long n) {
Matrix<T> C(A.size(), A.size());
for(int i = 0; i < A.size(); ++i) C[i][i] = 1;
while(n > 0) {
if(n & 1) C = C * A;
A = A * A;
n >>= 1;
}
return C;
}
template <typename T>
vector<T> pro(Matrix<T> A, vector<T> X){
vector<long long> ret(X.size(), 0);
for(int i=0; i<A.size(); ++i) {
for(int j=0; j<A[0].size(); ++j) {
ret[i] = (ret[i] + A[i][j] * X[j] % MOD) % MOD;
}
}
return ret;
}
long long powmod(long long x, long long n) {
long long ret = 1;
while(n > 0) {
if(n & 1) ret = ret * x % MOD;
x = x * x % MOD;
n >>= 1;
}
return ret;
}
using mat = Matrix<long long>;
using vec = vector<long long>;
int main() {
long long L, A, B;
cin >> L >> A >> B >> MOD;
int start = 0;
long long tmp = 1;
for(; start < 18; ++start) {
if(A >= tmp && A < tmp * 10) break;
tmp *= 10;
}
vec C(18);
long long prev = A - B, cnt = 0;
for(int i=start; i<18; ++i) {
C[i] = ((long long)pow(10, i + 1) - prev) / B;
if(prev + B * C[i] == (long long)pow(10, i + 1)) --C[i];
C[i] = min(C[i], L - cnt);
cnt += C[i];
if(cnt == L) break;
prev += B * C[i];
}
vec X = {0, A, B};
mat coeff(3, 3);
coeff[0] = {1, 1, 0};
coeff[1] = {0, 1, 1};
coeff[2] = {0, 0, 1};
for(int d=0; d<18; ++d) {
coeff[0][0] = powmod(10, d + 1);
X = pro(pow(coeff, C[d]), X);
}
cout << X[0] % MOD << endl;
} |
#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<ll,pll> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-9;
//const ll mod=1e9+7;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,0};
ll mod;
ll Pow(ll n,ll p){
ll r=1;
for(;p>0;p>>=1){
if(p&1) r=(r*n)%mod;
n=(n*n)%mod;
}
return r;
}
vvl mul(vvl A,vvl B){
vvl C(A.size(),vl(B[0].size()));
for(int i=0;i<A.size();i++) for(int k=0;k<B.size();k++) for(int j=0;j<B[0].size();j++) (C[i][j]+=A[i][k]*B[k][j])%=mod;
return C;
}
vvl pow(vvl A,ll n){
vvl B(A.size(),vl(A.size()));
for(int i=0;i<A.size();i++) B[i][i]=1;
while(n>0){
if(n&1) B=mul(B,A);
A=mul(A,A);
n>>=1;
}
return B;
}
ll n,a,d;
ll f(ll x){
return a+d*x;
}
int main(){
cin>>n>>a>>d>>mod;
ll t=1,res=0,tmp=1;
for(int i=0;i<17;i++) t*=10;
for(int i=17;i>=0;i--){
ll l=-1,r=n;
while(r-l>1){
ll m=(l+r)/2;
if(f(m)>=t) r=m;
else l=m;
}
ll A=f(r);
l=-1,r=n;
while(r-l>1){
ll m=(l+r)/2;
if(f(m)>=t*10) r=m;
else l=m;
}
ll B=f(r);
if(A<B){
ll N=(B-A)/d;
vvl a(3,vl(3));
a[0][0]=t*10%mod;
a[0][1]=a[1][1]=a[1][2]=a[2][2]=1;
a=pow(a,N);
ll sum=(A%mod*a[0][1]%mod+d%mod*a[0][2]%mod)%mod;
(res+=sum*tmp)%=mod;
(tmp*=Pow(Pow(10,N),i+1))%=mod;
}
t/=10;
}
cout<<res<<endl;
} |
#include<bits/stdc++.h>
#define lowbit(a) ((a)&(-(a)))
using namespace std;
void file(bool opt)
{
if (opt&&fopen("in.txt", "r"))
{
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
}
}
long long L, A, B;
long long mod;
long long ans = 0;
long long powt[19];
struct mat {
int val[3][3];
mat() { memset(val, 0, sizeof val); }
void init(int i)
{
memset(val, 0, sizeof val);
val[0][0] = powt[i] % mod, val[1][0] = val[1][1]= val[2][2] = 1;
val[2][1]=B%mod;
}
};
mat operator*(mat a, mat b)
{
mat c;
for (int i = 0; i<3; i++)
for (int j = 0; j<3; j++)
for (int k = 0; k<3; k++)
c.val[i][j] = (c.val[i][j] + 1ll * a.val[i][k] * b.val[k][j]) % mod;
return c;
}
void poww(long long L,long long R,int d)
{
long long n = (R - L) / B + 1;
mat res;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
res.val[i][j] = (i == j);
mat a;
a.init(d);
while (n)
{
if (n & 1)res = res * a;
n >>= 1;
a = a*a;
}
ans = (1ll * ans*res.val[0][0]%mod + L % mod*res.val[1][0] % mod + res.val[2][0]) % mod;
}
int main()
{
cin >> L >> A >> B >> mod;
powt[0] = 1;
for (int i = 1; i <= 18; i++)
powt[i] = powt[i - 1] * 10ll;
long long ed = A + B * (L - 1);
for (int d = 1; d <= 18; d++)
{
if (A < powt[d])
{
long long R = (powt[d] - 1 - A) / B * B + A;
R = min(R, ed);
poww(A, R, d);
if (R == ed)break;
A = R + B;
}
}
cout << ans << endl;
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Matrix = vector<vector<ll>>;
inline ll ceil_ll(ll x, ll y) { return (x + y - 1) / y; }
Matrix mulMatrix(const Matrix &A, const Matrix &B, const ll MOD) {
Matrix C(3, vector<ll>(3));
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
for (int k = 0; k < 3; ++k) {
(C[i][j] += (A[i][k] * B[k][j]) % MOD) %= MOD;
}
}
}
return C;
}
Matrix powMatrix(Matrix A, ll e, const ll MOD) {
vector<vector<ll>> X(3, vector<ll>(3));
X[0][0] = X[1][1] = X[2][2] = 1;
for ( ; 0 < e; e >>= 1) {
if (e & 1) X = mulMatrix(X, A, MOD);
A = mulMatrix(A, A, MOD);
}
return X;
}
using ull = unsigned long long;
ll fast_pow10(ull e, const ull MOD) {
ull a = 10, x = 1;
for ( ; 0 < e; e >>= 1) {
if (e & 1) (x *= a) %= MOD;
(a *= a) %= MOD;
}
return x;
}
int main() {
cin.tie(0); ios::sync_with_stdio(false);
// cout << setprecision(8) << setiosflags(ios::fixed);
constexpr int DIGITS = 19;
vector<ll> pow10(DIGITS);
pow10[0] = 1;
for (int i = 1; i < DIGITS; ++i)
pow10[i] = 10 * pow10[i - 1];
ll L, A, B, M;
cin >> L >> A >> B >> M;
vector<ll> begin(DIGITS), num(DIGITS);
for (ll d = 1; d < DIGITS; ++d) {
begin[d] = max(0ll, ceil_ll(pow10[d - 1] - A, B));
const ll end = min((pow10[d] - A - 1) / B, L - 1);
const ll s_l = A + B * begin[d], s_r = A + B * end;
if (pow10[d - 1] <= s_l && s_r < pow10[d] && begin[d] <= end)
num[d] = end - begin[d] + 1;
}
ll ans = 0;
for (ll d = 1; d < DIGITS; ++d) {
if (num[d] == 0) continue;
Matrix X(3, vector<ll>(3));
X[0][0] = pow10[d] % M; X[0][1] = 1;
X[1][1] = 1; X[1][2] = B % M;
X[2][2] = 1;
X = powMatrix(X, num[d], M);
const ll s0 = (A + B * begin[d]) % M;
const ll s = ((X[0][1] * s0) % M + X[0][2]) % M;
(ans *= fast_pow10((unsigned long long)d * num[d], M)) %= M;
(ans += s) %= M;
}
cout << ans << endl;
return 0;
}
|
#include <iostream>
#include <utility>
using namespace std;
__int128 mod_pow(__int128 x, __int128 k, __int128 mod){
__int128 ret = 1;
while(k){
if(k&1) ret *= x, ret %= mod;
x *= x, x %= mod;
k >>= 1;
}
return ret;
}
pair<__int128, __int128> rec(__int128 x, __int128 k, __int128 mod){
if(k == 1) return {1,0};
pair<__int128,__int128> p = rec(x,k/2,mod);
__int128 f = p.first, s = p.second;
__int128 f_ = (f*(1+mod_pow(x,k/2,mod))%mod)%mod;
if(k%2) f_ += mod_pow(x,k-1,mod), f_ %= mod;
__int128 s_ = (s + (((s+(f*(k/2))%mod)%mod)*mod_pow(x,k/2,mod))%mod)%mod;
if(k%2) s_ += (((k-1)%mod)*mod_pow(x,k-1,mod))%mod, s_ %= mod;
f_ %= mod, s_ %= mod;
return {f_,s_};
}
int main(){
long long L_, A_, B_, M_;
cin >> L_ >> A_ >> B_ >> M_;
__int128 L = L_, A = A_, B = B_, M = M_;
A += B*(L-1);
B *= -1;
constexpr int max_len = 18;
__int128 s = 0;
__int128 ans = 0;
__int128 D[max_len+1];
D[0] = 1;
for(int k = 0; k < max_len; ++k) D[k+1] = (D[k]*10);
__int128 prev_r = 0;
for(int k = max_len; k >= 0; --k){
__int128 d_ = D[k];
if(d_ > A) continue;
__int128 l = prev_r, r = (A-d_)/(-B) + 1;
r = max(l,r);
r = min(L,r);
// cerr << k+1 << " " << l << " " << r << endl;
// cerr << s << endl;
if(l < r){
pair<__int128,__int128> p = rec(mod_pow(10,k+1,M),r-l,M);
__int128 t = (p.first*((A%M+(((B%M+M)%M)*(l%M))%M)%M))%M;
t += (p.second*((B%M+M)%M))%M;
t %= M;
t *= mod_pow(10,s,M);
ans += t%M;
ans %= M;
s += (r-l)*(k+1);
}
prev_r = r;
}
cout << (long long)ans << endl;
}
|
#include<bits/stdc++.h>
using namespace std;
using LL = long long;
const int NDigit = 19;
int mod, pw10[NDigit];
int add(int a, int b) { return a + b >= mod ? a + b - mod : a + b; }
int mul(int a, int b) { return (int)( (LL)a * b % mod); }
LL nTerm, a, b;
struct Matrix {
int nR, nC;
vector<vector<int> > a;
Matrix(int _nR, int _nC) : nR(_nR), nC(_nC) {
a.assign(nR, vector<int>(nC, 0) );
}
Matrix operator*(const Matrix &_) const {
Matrix ret(nR, _.nC);
for (int i = 0; i < ret.nR; ++i) {
for (int j = 0; j < ret.nC; ++j) {
for (int k = 0; k < nC; ++k) ret.a[i][j] = add(ret.a[i][j], mul(a[i][k], _.a[k][j]) );
}
}
return ret;
}
Matrix binpw(LL exp) const {
Matrix M = *this;
assert(nR == nC);
Matrix ret(nR, nC);
for (int i = 0; i < nR; ++i) ret.a[i][i] = 1;
for (; exp; exp >>= 1, M = M * M) if (exp & 1) ret = ret * M;
return ret;
}
void debug() {
for (int i = 0; i < nR; ++i) {
for (int j = 0; j < nC; ++j) cerr << a[i][j] << ' '; cerr << '\n';
}
cerr << "====\n";
}
};
int nDigit(LL num) {
int ret = 0;
while (num) { ++ret; num /= 10; }
return ret;
}
int main() {
scanf(" %lld %lld %lld %d", &nTerm, &a, &b, &mod);
pw10[0] = 1;
for (int i = 1; i < NDigit; ++i) pw10[i] = mul(pw10[i - 1], 10);
Matrix cur(1, 3);
cur.a[0][0] = (int)(b % mod); cur.a[0][1] = (int)(a % mod); cur.a[0][2] = (int)(a % mod);
for (LL prv = 0; prv + 1 < nTerm; ) {
LL lNxt = prv + 1, rNxt = nTerm - 1;
while (lNxt < rNxt) {
LL mNxt = (lNxt + rNxt + 1) >> 1;
if (nDigit(a + b * mNxt) == nDigit(a + (prv + 1) * b) ) lNxt = mNxt;
else rNxt = mNxt - 1;
}
LL nxt = lNxt;
Matrix tranMatrix(3, 3);
tranMatrix.a[0][0] = tranMatrix.a[0][1] = tranMatrix.a[0][2] = tranMatrix.a[1][1] = tranMatrix.a[1][2] = 1;
tranMatrix.a[2][2] = pw10[nDigit(a + nxt * b)];
tranMatrix = tranMatrix.binpw(nxt - prv);
cur = cur * tranMatrix;
prv = nxt;
}
printf("%d\n", cur.a[0][2]);
return 0;
}
|
/*
[abc129] F - Takahashi's Basics in Education and Learning
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
ll L, A, B;
int MOD;
class gf {
public:
int n;
gf() : n(0) {}
gf(int n) : n(n % MOD) {}
gf operator+(const gf x) const { return gf((n + x.n) % MOD); }
gf operator*(const gf x) const { return gf((1LL * n * x.n) % MOD); }
gf &operator+=(const gf x) { return *this = (*this + x); }
gf &operator*=(const gf x) { return *this = (*this * x); }
};
typedef gf Number;
typedef vector<Number> Array;
typedef vector<Array> Matrix;
Matrix identity(int n) {
Matrix A(n, Array(n));
for (int i = 0; i < n; i++) {
A[i][i] = 1;
}
return A;
}
Array mul(const Matrix &A, const Array &x) {
Array y(A.size());
for (int i = 0; i < (int)A.size(); i++) {
for (int j = 0; j < (int)x.size(); j++) {
y[i] += A[i][j] * x[j];
}
}
return y;
}
Matrix mul(const Matrix &A, const Matrix &B) {
Matrix C(A.size(), Array(B[0].size()));
for (int i = 0; i < (int)C.size(); i++) {
for (int j = 0; j < (int)C[i].size(); j++) {
for (int k = 0; k < (int)A[i].size(); k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
Matrix pow(const Matrix &A, ll e) {
Matrix AA = A;
Matrix ans = identity(A.size());
for (; e > 0; e >>= 1) {
if (e & 1) {
ans = mul(ans, AA);
}
AA = mul(AA, AA);
}
return ans;
}
const Number eps = 1e-8;
const int D = 18;
ll c[D + 1];
ll solve() {
for (ll d = 1, dec = 10; d <= D; d++, dec *= 10) {
c[d] = min(L, max(dec - A + B - 1, 0LL) / B);
}
Array v = {0, (int)(A % (ll)MOD), 1};
gf dec = 10;
for (int d = 1; d <= D; d++) {
Matrix A = {{dec, 1, 0}, {0, 1, (int)(B % (ll)MOD)}, {0, 0, 1}};
v = mul(pow(A, c[d] - c[d - 1]), v);
dec *= 10;
}
gf ans = v[0];
return ans.n;
}
int main() {
cin >> L >> A >> B >> MOD;
cout << solve() << endl;
return 0;
}
|
#include <iostream>
#include <vector>
using Matrix = std::vector<std::vector<long long>>;
int main() {
long long L, A, B, M;
std::cin >> L >> A >> B >> M;
std::vector<long long> C(19);
long long p = 1;
for (int d = 1; d < 19; d++) {
p *= 10;
if (p - 1 < A)
continue;
C[d] = std::min(L, (p - 1 - A) / B + 1);
}
auto mul = [&M](Matrix& m1, Matrix& m2) {
Matrix res(3, std::vector<long long>(3));
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++) {
res[i][j] += m1[i][k] * m2[k][j] % M;
res[i][j] %= M;
}
return res;
};
auto pow = [&mul](Matrix& m, long long n) {
Matrix res = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
for (; n; n >>= 1) {
if (n & 1)
res = mul(res, m);
m = mul(m, m);
}
return res;
};
std::vector<long long> ans = {0, A % M, 1};
p = 1;
for (int d = 1; d < 19; d++) {
p = p * 10 % M;
Matrix m = {{p, 0, 0}, {1, 1, 0}, {0, B % M, 1}};
m = pow(m, C[d] - C[d - 1]);
std::vector<long long> res = {0, 0, 0};
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++) {
res[i] += ans[j] * m[j][i] % M;
res[i] %= M;
}
ans = res;
}
std::cout << ans[0] << "\n";
} |
#include <bits/stdc++.h>
using namespace std;
typedef signed long long ll;
#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define ITR(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
//-------------------------------------------------------
ll L,A,B,mo;
ll F[20];
ll num[20];
ll p10[20];
ll S[20];
ll modpow(ll a, __int128 n) {
ll r=1;a%=mo;
while(n) r=r*((n%2)?a:1)%mo,a=a*a%mo,n>>=1;
return r;
}
ll hoge(ll len,ll p) {
if(len==0) return 0;
if(len==1) return 1;
ll a=modpow(p,len/2);
ll v=hoge(len/2,p);
if(len%2==0) {
return v*(1+a)%mo;
}
else {
return (v*(1+a)+a*a)%mo;
}
}
ll hoge2(ll len,ll p) {
if(len<=0) return 0;
if(len==1) return 1;
if(len%2==0) {
ll a=modpow(p,len/2);
ll v=hoge2(len/2,p);
return (v*(1+a)+(len/2)%mo*hoge(len/2,p))%mo;
}
else {
return (hoge2(len-1,p)+hoge(len,p))%mo;
}
}
void solve() {
int i,j,k,l,r,x,y; string s;
cin>>L>>A>>B>>mo;
p10[0]=1;
FOR(i,19) p10[i+1]=p10[i]*10;
ll w=L;
ll v=A;
for(i=1;i<=19;i++) if(v<p10[i] && w) {
ll d=min(w,(p10[i]-v+B-1)/B);
F[i]=v;
num[i]=d;
v+=B*d;
w-=d;
}
ll c=1;
ll ret=0;
for(i=19;i>=1;i--) if(num[i]) {
ll p=p10[i]%mo;
ll n=num[i];
ll a=F[i];
ll r=(F[i]%mo*hoge(n,p)+B%mo*hoge2(n-1,p))%mo;
ret+=r*c%mo;
c=c*modpow(10,__int128(i)*num[i])%mo;
}
cout<<ret%mo<<endl;
}
int main(int argc,char** argv){
string s;int i;
if(argc==1) ios::sync_with_stdio(false), cin.tie(0);
FOR(i,argc-1) s+=argv[i+1],s+='\n'; FOR(i,s.size()) ungetc(s[s.size()-1-i],stdin);
cout.tie(0); solve(); return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define all(ppp) ppp.begin(),ppp.end()
#define out(ppp) cout<<(ppp)<<endl
#define out1(ppp) cout<<(ppp)
#define MAX_CHAR 256
#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define REP(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define pb push_back
#define lint ll
typedef long double ld;
typedef complex<ld> cd;
ll MOD;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<vi> vvi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
typedef vector<vpi> vvpi;
typedef set<pi> spi;
const int INF=INT_MAX;
vector<vector<lint>> matmul(const vector<vector<lint>> &A, const vector<vector<lint>> &B, lint mod=MOD){
int H = A.size(), W = B[0].size(), K = B.size();
vector<vector<lint>> C(H, vector<lint>(W));
REP(i, H) REP(j, W) REP(k, K) (C[i][j] += A[i][k] * B[k][j]) %= mod;
return C;
}
vector<vector<lint>> matpower(vector<vector<lint>> X, lint n, lint mod=MOD){
vector<vector<lint>> res(X.size(), vector<lint>(X.size()));
REP(i, res.size()) res[i][i] = 1;
while (n)
{
if (n & 1) res = matmul(res, X, mod);
X = matmul(X, X, mod); n >>= 1;
}
return res;
}
lint power(lint x, lint n){
lint ans = 1;
while (n>0)
{
if (n & 1) (ans *= x) %= MOD;
(x *= x) %= MOD;
n >>= 1;
}
return ans;
}
ll sol(ll len,ll A,ll B,ll amari){
if(!len){
return amari;
}
ll d=to_string(A).length();
ll m=1;
F0R(i,d){
m*=10;
}
ll n_term=min((m-1-A)/B+1,len);
vector<vector<ll>> trans{{power(10,d),1,0},{0,1,1},{0,0,1}};
trans=matpower(trans,n_term);
return sol(len-n_term,A+B*n_term,B,(trans[0][0]*(amari%MOD)%MOD+trans[0][1]*(A%MOD)+trans[0][2]*(B%MOD)%MOD)%MOD);
}
void solve(){
ll l,A,B;
cin>>l>>A>>B>>MOD;
ll ret=sol(l,A,B,0);
out(ret);
}
int main(){
solve();
return 0;
} |
#include<bits/stdc++.h>
using namespace std;
int md;
struct mat{
int a[3][3],h,w;
mat(){memset(a,0,sizeof(a));h=w=0;}
mat operator*(mat u)const
{
mat res;
res.h=h;res.w=u.w;
for(int i=0;i<h;i++)
{
for(int j=0;j<u.w;j++)
{
for(int k=0;k<w;k++)
{
res.a[i][j]=(res.a[i][j]+1LL*a[i][k]*u.a[k][j]%md)%md;
}
}
}
return res;
}
};
mat qmul(mat x,long long p)
{
mat res;
res.h=x.h;
res.w=x.w;
for(int i=0;i<x.h;i++)res.a[i][i]=1;
for(;p;p>>=1,x=x*x)if(p&1)res=res*x;
return res;
}
long long l,a,b;
long long pw[19];
int ans;
int main()
{
scanf("%lld%lld%lld%d",&l,&a,&b,&md);
int s=0;
long long t=a;
do
{
t/=10;
s++;
}
while(t);
pw[0]=1;
for(int i=1;i<=18;i++)pw[i]=pw[i-1]*10;
long long st=0;
for(int i=s;i<=18 && st<l;i++)
{
long long L=st,R=l-1;
while(L<=R)
{
long long mid=(L+R)>>1;
if(a+mid*b<pw[i])L=mid+1;else R=mid-1;
}
mat tmp;
tmp.h=1;tmp.w=3;
tmp.a[0][0]=ans;tmp.a[0][1]=(a+st*b)%md;tmp.a[0][2]=b%md;
mat dp;
dp.h=dp.w=3;
dp.a[0][0]=pw[i]%md;
dp.a[1][0]=1;
dp.a[1][1]=1;
dp.a[2][1]=1;
dp.a[2][2]=1;
tmp=tmp*qmul(dp,L-st);
ans=tmp.a[0][0];
st=L;
}
printf("%d",ans);
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<ll>>;
long long P;
ll power(ll e, ll x) {
if (x == 0) return 1;
if (x % 2 == 0) return power((e * e) % P, x / 2);
return (e * power(e, x - 1)) % P;
}
vvl mul(vvl a, vvl b) {
int n = a.size();
int m = b[0].size();
vvl ret(n, vector<ll>(m));
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
for (int k = 0; k < a[i].size(); k++) {
ret[i][j] += (a[i][k] * b[k][j]) % P;
ret[i][j] %= P;
}
}
}
return ret;
}
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
ll l, a, b;
cin >> l >> a >> b >> P;
ll p10[1010] = {0};
p10[0] = 1;
for (int i = 0; i < 19; i++) p10[i + 1] = p10[i] * 10;
ll ans = 0;
for (int first = 1; first <= 19 && l > 0; first++) {
ll mx = p10[first];
if (mx <= a) continue;
ll sz = min(l, (mx - a + b - 1) / b);
vvl v({{ans, a % P, 1}});
vvl S({
{p10[first] % P, 0, 0},
{1, 1, 0},
{0, b % P, 1},
});
vvl I({{1, 0, 0},
{0, 1, 0},
{0, 0, 1}});
for (ll k = sz; k > 0; k >>= 1) {
if (k % 2 == 1) {
I = mul(S, I);
}
S = mul(S, S);
}
S = mul(v, I);
ans = S[0][0];
l -= sz;
a += b * sz;
}
cout << ans << endl;
return 0;
}
|
#include<iostream>
#include<cstdio>
#include<cstring>
#include <cstdlib>
#include <math.h>
#include <cmath>
#include<cctype>
#include<string>
#include<set>
#include<iomanip>
#include <map>
#include<algorithm>
#include <functional>
#include<vector>
#include<climits>
#include<stack>
#include<queue>
#include<bitset>
#include <deque>
#include <climits>
#include <typeinfo>
#include <utility>
using namespace std;
using ll = long long;
template<typename T>using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
const ll inf = 1LL << 60;
#define all(x) (x).begin(),(x).end()
#define puts(x) cout << x << endl
#define rep(i,m,n) for(ll i = m;i < n;++i)
#define pb push_back
#define fore(i,a) for(auto &i:a)
#define rrep(i,m,n) for(ll i = m;i >= n;--i)
ll L, A, B, M;
vector<vector<ll>>matrix_mul(vector<vector<ll>>a, vector<vector<ll>>b) {
vector<vector<ll>>res(a.size(),vector<ll>(b[0].size()));
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < b[0].size();j++) {
ll temp = 0;
for (int k = 0; k < b.size(); k++) {
a[i][k] %= M;
b[k][j] %= M;
temp += (a[i][k] * b[k][j]) % M;
temp %= M;
}
res[i][j] = temp;
}
}
return res;
}
vector<vector<ll>>matrix_pow(vector<vector<ll>>a,ll n) {
vector<vector<ll>>E(a.size(), vector<ll>(a.size(),0));
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < a.size(); j++) {
E[i][j] = (i == j);
}
}
while (n > 0) {
if (n & 1)E = matrix_mul(E, a);
a = matrix_mul(a, a);
n >>= 1;
}
return E;
}
ll po(ll n) {
ll ret = 1;
for (int i = 0; i < n; i++)ret *= 10LL;
return ret;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> L >> A >> B >> M;
ll pre = -1;
vector<vector<ll>>cur(3, vector<ll>(1, 0));
cur[1][0] = A;
cur[2][0] = 1;
for (int i = 1; i <= 18; i++) {
vector<vector<ll>>M(3, vector<ll>(3, 0));
M[0] = { po(i),1,0 };
M[1] = { 0,1,B };
M[2] = { 0,0,1 };
if (A + (L - 1)*B < po(i)) {
cur = matrix_mul(matrix_pow(M,L-1-pre),cur);
break;
}
ll ok = pre, ng = L - 1;
while (ng - ok > 1) {
ll mid = (ng + ok) / 2LL;
if (A + mid * B < po(i))ok = mid;
else ng = mid;
}
vector<vector<ll>>temp = matrix_pow(M, ok - pre);
cur = matrix_mul(temp, cur);
pre = ok;
}
puts(cur[0][0]);
return 0;
} |
#include <bits/stdc++.h>
#include<iostream>
#include<fstream>
#define ll long long
using namespace std;
ll nDigit(ll n){
if(n<10) return 1;
else return 1 + nDigit(n/10);
}
ll cnt(ll L, ll A, ll B){
ll N = nDigit(A);
ll left = 0, right = L;
while(right - left > 1){
ll mid = (right+left)/2;
if(N == nDigit(A+B*mid)){
left = mid;
}else{
right = mid;
}
}
return left+1;
}
vector<vector<ll>> multiple(vector<vector<ll>> K, vector<vector<ll>> L, ll mod){
int S = K.size();
vector<vector<ll>> ret = vector<vector<ll>>(S, vector<ll>(S,0));
for(int i=0; i<S; i++) for(int j=0; j<S; j++){
for(int k=0; k<S; k++){
ret[i][j] = (ret[i][j]%mod + (K[i][k]%mod)*(L[k][j]%mod)%mod) % mod;
}
}
return ret;
}
vector<vector<ll>> mod_pow(vector<vector<ll>> K, ll c, ll mod){
int S = K.size();
vector<vector<ll>> ret(S, vector<ll>(S,0));
for(int i=0; i<S; i++){
ret[i][i] = 1;
}
if(c==0) return ret;
ret = mod_pow(multiple(K, K, mod), c/2, mod);
if(c%2==1){
ret = multiple(K, ret, mod);
}
return ret;
}
int main(){
ll L, A, B, mod;
cin >> L >> A >> B >> mod;
ll ans = 0;
while(L>0){
ll c = cnt(L, A, B);
ll p = 1;
for(ll i=0; i<nDigit(A); i++){
p*=10;
p%=mod;
}
vector<ll> b = {ans, A%mod, 1};
vector<vector<ll>> K = {{p, 0, 0},
{1, 1, 0},
{0, B%mod, 1}};
K = mod_pow(K, c, mod);
vector<ll> a(3);
a[0] = (b[0] * K[0][0] + b[1] * K[1][0] + b[2] * K[2][0]) % mod;
a[1] = (b[0] * K[0][1] + b[1] * K[1][1] + b[2] * K[2][1]) % mod;
a[2] = (b[0] * K[0][2] + b[1] * K[1][2] + b[2] * K[2][2]) % mod;
ans = a[0];
L -= c;
A += B*c;
}
cout << ans << endl;
}
|
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll L,a,b,mod;
struct Matric
{
ll a[3][3];
Matric(){memset(a,0,sizeof(a));}
Matric operator*(const Matric&o)const
{
Matric ans;
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
for(int k=0;k<3;k++)
ans.a[i][j]=(ans.a[i][j]+a[i][k]*o.a[k][j]%mod)%mod;
return ans;
}
};
Matric Mqpow(Matric a,ll n)
{
Matric ans;
ans.a[0][0]=ans.a[1][1]=ans.a[2][2]=1;
while(n)
{
if(n&1) ans=ans*a;
a=a*a;
n>>=1;
}
return ans;
}
ll qpow(ll a,ll n)
{
ll ans=1;
while(n)
{
if(n&1) ans=ans*a%mod;
a=a*a%mod;
n>>=1;
}
return ans;
}
int getlen(ll x)
{
int ans=0;
while(x)
{
x/=10;
ans++;
}
return ans;
}
ll getpos(int x)
{
ll l=1,r=L,ans=1;
while(l<=r)
{
ll m=l+r>>1;
if(getlen(a+(m-1)*b)<=x) ans=m,l=m+1;
else r=m-1;
}
return ans;
}
/*
si=s(i-1)*qpow(10,i)+qi+B;
gi=g(i-1)+B;
|10i 1 1| |si-1|
|0 1 1| |gi-1|
|0 0 1| |B|
*/
int main()
{
scanf("%lld%lld%lld%lld",&L,&a,&b,&mod);
//mod=1e9+7;
ll ans=a%mod,res=a%mod,now=1;
for(int i=1;i<=18;i++)
{
ll p=getpos(i);
if(p==now) continue;
Matric A;
A.a[0][0]=qpow(10,i);A.a[0][1]=0;A.a[0][2]=0;
A.a[1][0]=1;A.a[1][1]=1%mod;
A.a[2][1]=b%mod;A.a[2][2]=1;
A=Mqpow(A,p-now);
ans=(A.a[0][0]*ans%mod+(res+b)%mod*A.a[1][0]%mod+A.a[2][0]%mod)%mod;
res=(res+b*(p-now))%mod;
now=p;
//cout<<ans<<endl;
}
printf("%lld\n",ans);
}
|
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll L,a,b,mod;
struct Matric
{
ll a[3][3];
Matric(){memset(a,0,sizeof(a));}
Matric operator*(const Matric&o)const
{
Matric ans;
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
for(int k=0;k<3;k++)
ans.a[i][j]=(ans.a[i][j]+a[i][k]*o.a[k][j]%mod)%mod;
return ans;
}
};
Matric Mqpow(Matric a,ll n)
{
Matric ans;
ans.a[0][0]=ans.a[1][1]=ans.a[2][2]=1;
while(n)
{
if(n&1) ans=ans*a;
a=a*a;
n>>=1;
}
return ans;
}
ll qpow(ll a,ll n)
{
ll ans=1;
while(n)
{
if(n&1) ans=ans*a%mod;
a=a*a%mod;
n>>=1;
}
return ans;
}
int getlen(ll x)
{
int ans=0;
while(x)
{
x/=10;
ans++;
}
return ans;
}
ll getpos(int x)
{
ll l=1,r=L,ans=1;
while(l<=r)
{
ll m=l+r>>1;
if(getlen(a+(m-1)*b)<=x) ans=m,l=m+1;
else r=m-1;
}
return ans;
}
/*
si=s(i-1)*qpow(10,i)+qi+B;
gi=g(i-1)+B;
|10i 1 1| |si-1|
|0 1 1| |gi-1|
|0 0 1| |B|
*/
int main()
{
scanf("%lld%lld%lld%lld",&L,&a,&b,&mod);
//mod=1e9+7;
ll ans=a%mod,res=a%mod,now=1;
for(int i=1;i<=18;i++)
{
ll p=getpos(i);
if(p==now) continue;
Matric A;
A.a[0][0]=qpow(10,i);A.a[0][1]=0;A.a[0][2]=0;
A.a[1][0]=1;A.a[1][1]=1;
A.a[2][0]=1;A.a[2][1]=1;A.a[2][2]=1;
A=Mqpow(A,p-now);
ans=(A.a[0][0]*ans%mod+res*A.a[1][0]%mod+b%mod*A.a[2][0]%mod)%mod;
res=(res+b*(p-now))%mod;
now=p;
//cout<<ans<<endl;
}
printf("%lld\n",ans);
}
|
#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ll;
int Mod;
struct Matrix {
int n, m;
ll a[10][10];
Matrix(int _n = 0, int _m = 0, int x = 0) {
memset(a, 0, sizeof a);
n = _n, m = _m;
for (int i = 1; i <= n; ++i)
a[i][i] = x;
}
Matrix operator * (const Matrix &b) {
Matrix res = Matrix(n, b.m);
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= m; ++j) if (a[i][j])
for (int k = 1; k <= b.m; ++k)
(res.a[i][k] += a[i][j] * b.a[j][k] % Mod) %= Mod;
return res;
}
Matrix operator ^ (ll k) {
Matrix res = Matrix(n, n, 1), x = *this;
while (k) {
if (k & 1) res = res * x;
x = x * x;
k >>= 1;
}
return res;
}
};
inline ll fsp(ll x, ll k) {
x = x % Mod;
ll res = 1;
while (k) {
if (k & 1) res = res * x % Mod;
x = x * x % Mod;
k >>= 1;
}
return res;
}
int main() {
ll n, a, d;
cin >> n >> a >> d >> Mod;
ll b = 1, ans = 0;
for (int i = 1; i <= 18; ++i, b = b * 10) {
ll L = b, R = 10 * b - 1, s;
if (R < a) continue;
if (L <= a) L = 1;
else L = (L - a - 1) / d + 2;
R = (R - a) / d + 1;
L = max(L, 1ULL), R = min(R, 1ULL * n);
if (L > R) continue;
s = (a + (L - 1) * (d));
s %= Mod;
Matrix base = Matrix(3, 3, 0);
base.a[1][1] = b * 10 % Mod;
base.a[2][1] = base.a[2][2] = base.a[3][2] = base.a[3][3] = 1;
base = base ^ (R - L + 1);
ans = ((ans * fsp(b * 10, (R - L + 1)) % Mod + s % Mod * base.a[2][1] % Mod) % Mod + d % Mod * base.a[3][1] % Mod) % Mod;
}
cout << ans << endl;
return 0;
}
|
#include<iostream>
#include<string>
#include<iomanip>
#include<cmath>
#include<vector>
#include<algorithm>
using namespace std;
#define int long long
#define rep(i,n) for(int i = 0; i < (n); i++)
#define INF ((long long)1e18)
#define endl "\n"
#define yn(f) ((f)?"Yes":"No")
#define YN(f) ((f)?"YES":"NO")
#define MAX
long long MOD;
template<typename type>
vector<vector<type>> product(vector<vector<type>> &a, vector<vector<type>> &b){
vector<vector<type>> res(a.size(),vector<type>(b[0].size(),0));
for(int i = 0; i < a.size(); i++){
for(int j = 0; j < b[0].size(); j++){
for(int k = 0; k < b.size(); k++){
res[i][j] += a[i][k]*b[k][j];
res[i][j] %= MOD;
}
}
}
return res;
}
template<typename type>
vector<vector<type>> matrix_power(vector<vector<type>> matrix, long long n){
vector<vector<type>> res(matrix.size(), vector<type>(matrix.size(),0));
for(int i = 0; i < matrix.size(); i++) res[i][i] = 1;
for( ; n > 0; n >>= 1){
if(n&1) res = product(res,matrix);
matrix = product(matrix,matrix);
}
return res;
}
int check(int num){
int con = 0;
while(num) con++, num /= 10;
return con;
}
signed main(){
cin.tie(0);
ios::sync_with_stdio(false);
cout<<fixed<<setprecision(10);
vector<vector<int>> ans(3,vector<int>(1,0));
long long L, A, B;
int b = -1;
cin>>L>>A>>B>>MOD;
ans[0][0] = 0;
ans[1][0] = A;
ans[2][0] = 1;
for(int i = 1, power = 10; i <= 18; i++, power *= 10){
vector<vector<int>> matrix(3,vector<int>(3,0));
int d = 0;
int m = 0, l = 0, h = L;
while(l + 1 < h){
int m = (l + h)/2;
if(check(A + m*B) > i){
h = m;
} else {
l = m;
}
}
if(check(A + l*B) < i) continue;
d = l - b;
b = l;
matrix[0][0] = power%MOD;
matrix[0][1] = matrix[1][1] = matrix[2][2] = 1;
matrix[1][2] = B;
matrix = matrix_power(matrix, d);
ans = product(matrix, ans);
}
cout<<ans[0][0]<<endl;
return 0;
} |
#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <assert.h>
#include <memory.h>
#include <queue>
#include <string.h>
#include <map>
using namespace std;
#define ll long long
ll add(ll x,ll y,ll mod) {
x%=mod;
y%=mod;
return ((x+y)%mod+mod)%mod;
}
ll mul(ll x,ll y,ll mod) {
x%=mod;
y%=mod;
return x*y%mod;
}
ll mypow(ll x,ll c,ll mod) {
ll ret = 1;
while(c>0) {
if(c&1) {
ret = mul(ret,x,mod);
}
c/=2;
x = mul(x,x,mod);
}
return ret;
}
int getLen(ll x) {
int ret = 0;
while(x>0) {
x/=10;
++ret;
}
return ret;
}
#define mat vector<vector<ll> >
mat mul(mat x,mat y,ll mod) {
mat R = mat(x.size(),vector<ll>(x.size(),0LL));
for(int i=0;i<x.size();++i) {
for(int j=0;j<x.size();++j) {
for(int k=0;k<x.size();++k) {
R[i][j] = add(R[i][j], mul(x[i][k],y[k][j],mod),mod);
}
}
}
return R;
}
mat matPow(mat x,ll cc,ll mod) {
int n = x.size();
mat R = mat(n,vector<ll>(n,0LL));
for(int i=0;i<n;++i) {
R[i][i] = 1;
}
while(cc>0) {
if(cc&1) {
R = mul(R, x,mod);
}
x = mul(x,x,mod);
cc/=2;
}
return R;
}
void solve() {
ll L,A,B,mod;
scanf("%lld %lld %lld %lld ",&L,&A,&B,&mod);
ll firstInd = 1;
ll ret = 0;
while(firstInd<=L) {
ll l = firstInd,r = L,mid;
int len = getLen(A + (firstInd-1)*B);
while(l<r) {
mid = (l+r+1)/2;
ll tmp = A + (mid-1)*B;
if(getLen(tmp)!=len) {
r = mid-1;
} else {
l = mid;
}
}
mat R = mat(3,vector<ll>(3,0LL));
R[0][0] = mypow(10,len,mod);
R[1][0] = 1;
R[1][1] = 1;
R[2][1] = 1;
R[2][2] = 1;
ll X = A + (firstInd-1)*B;
R = matPow(R,l-firstInd+1,mod);
ll tmp = add(add(mul(ret,R[0][0],mod),mul(X,R[1][0],mod),mod),mul(B,R[2][0],mod) ,mod);
ret = tmp;
firstInd = l+1;
}
printf("%lld\n", ret);
}
int main() {
//freopen("input.txt","r",stdin);
solve();
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
template<typename A, typename B> inline bool chmax(A &a, B b) { if (a<b) { a=b; return 1; } return 0; }
template<typename A, typename B> inline bool chmin(A &a, B b) { if (a>b) { a=b; return 1; } return 0; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = 0;
//---------------------------------//
ll mod_pow(ll x, ll n, ll mod = MOD) {
if (n == 0) return 1;
ll res = mod_pow(x * x % mod, n / 2, mod);
if (n & 1) res = res * x % mod;
return res;
}
ll f(ll l, ll base, ll M) {
if (l <= 1) return l;
ll res = f(l / 2, base, M) * (mod_pow(base, l / 2, M) + 1) % M;
if (l & 1) res = (res * base + 1) % M;
return res;
}
ll g(ll l, ll base, ll M) {
if (l <= 1) return 0;
ll res = g(l / 2, base, M) * (mod_pow(base, l / 2, M) + 1) % M + f(l / 2, base, M) * ((l / 2) % M) % M;
res %= M;
if (l & 1) res = (res * base + l - 1) % M;
return res;
}
int main() {
ll L, A, B, M;
cin >> L >> A >> B >> M;
ll cnt[19] = {};
ll sum = 0;
for (ll k = 1, p10 = 1; k <= 18; k++, p10 *= 10) {
// [p10, p10 * 10)の個数をcnt[k]
ll rc = p10 * 10 - 1 >= A ? (p10 * 10 - A - 1) / B + 1 : 0;
ll lc = p10 - 1 >= A ? (p10 - A - 1) / B + 1 : 0;
ll cur = rc - lc;
if (sum + cur >= L) cur = L - sum;
cnt[k] = cur;
sum += cur;
}
A %= M; B %= M;
sum = 0;
ll num[19] = {};
FOR(k, 1, 19) {
ll base = mod_pow(10, k, M);
num[k] = (A + B*sum) % M * f(cnt[k], base, M) % M + B * g(cnt[k], base, M) % M;
num[k] %= M;
sum = (sum + cnt[k]) % M;
}
ll ans = 0;
FOR(k, 1, 19) {
REP(i, k) ans = ans * mod_pow(10, cnt[k], M) % M;
ans = (ans + num[k]) % M;
}
cout << ans << endl;
return 0;
}
|
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define rep1(i, n) for(int i = 1; i <= (n); i++)
#define co(x) cout << (x) << "\n"
#define cosp(x) cout << (x) << " "
#define ce(x) cerr << (x) << "\n"
#define cesp(x) cerr << (x) << " "
#define pb push_back
#define mp make_pair
#define Would
#define you
#define please
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
ll L, A, B, M;
cin >> L >> A >> B >> M;
ll D[18] = {};
ll keta[19];
rep(i, 19) keta[i] = pow(10, i);
ll goukei = 0;
rep(i, 18) {
ll k1 = keta[i] - A - B - 1;
if (k1 < 0) k1 = -1;
else k1 /= B;
ll k2 = keta[i + 1] - A - B - 1;
if (k2 < 0) k2 = -1;
else k2 /= B;
ll k3 = k2 - k1;
if (k3 + goukei > L - 1) k3 = L - 1 - goukei;
D[i] = k3;
goukei += k3;
ce(D[i]);
}
ll Mat[18][3][3][60] = {};
rep(i, 18) {
ll kari = 1;
rep(j, i + 1) kari = kari * 10 % M;
Mat[i][0][0][0] = kari;
Mat[i][0][1][0] = B % M;
Mat[i][0][2][0] = A % M;
Mat[i][1][0][0] = 0;
Mat[i][1][1][0] = 1;
Mat[i][1][2][0] = 1;
Mat[i][2][0][0] = 0;
Mat[i][2][1][0] = 0;
Mat[i][2][2][0] = 1;
rep(j, 59) {
rep(x, 3) rep(y, 3) {
rep(z, 3) Mat[i][x][y][j + 1] += Mat[i][x][z][j] * Mat[i][z][y][j] % M;
Mat[i][x][y][j + 1] %= M;
}
}
}
ll V1 = A % M;
ll V2 = 1;
ll V3 = 1;
rep(i, 18) {
rep(j, 60) {
if (D[i] >> j & 1) {
ll V4, V5, V6;
V4 = (Mat[i][0][0][j] * V1 + Mat[i][0][1][j] * V2 + Mat[i][0][2][j] * V3) % M;
V5 = (Mat[i][1][0][j] * V1 + Mat[i][1][1][j] * V2 + Mat[i][1][2][j] * V3) % M;
V6 = (Mat[i][2][0][j] * V1 + Mat[i][2][1][j] * V2 + Mat[i][2][2][j] * V3) % M;
V1 = V4;
V2 = V5;
V3 = V6;
ce(V1);
}
}
}
co(V1);
Would you please return 0;
} |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> ii;
typedef tuple<ll, ll, ll> iii;
typedef vector<ll> vi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<vi> vvi;
typedef vector<vii> vvii;
#define REP(i,n) for (ll i = 0; i < n; ++i)
#define REPR(i,n) for (ll i = n-1; i >= 0; --i)
#define FOR(i,m,n) for (ll i = m; i < n; ++i)
#define FORR(i,m,n) for (ll i = n-1; i >= m; --i)
#define FORE(x,xs) for (const auto& x : xs)
#define PB push_back
#define MP make_pair
#define MT make_tuple
#define ALL(v) v.begin(), v.end()
vvi mult(vvi a, vvi b, ll MOD) {
int l = a[0].size();
int m = a.size(), n = b[0].size();
vvi res(m, vi(n));
REP (i, m) REP (j, n) REP (k, l) {
res[i][j] += a[i][k] * b[k][j];
res[i][j] %= MOD;
}
return res;
}
vvi pow(vvi a, ll k, ll MOD) {
int n = a.size();
vvi res(n, vi(n));
REP (i, n) res[i][i] = 1;
while(k) {
if (k&1) res = mult(res,a,MOD);
a = mult(a,a,MOD);
k >>= 1;
}
return res;
}
ll L, A, B, MOD;
ll digit[19];
ll s(ll n) {
return A + B * n;
}
int solve() {
ll k = 1;
REP (i, 18) {
ll lo = -1, hi = L;
while (hi - lo > 1ll) {
ll mid = (hi+lo)/2;
if (s(mid) >= k*10) hi = mid;
else lo = mid;
}
digit[i] = hi;
k *= 10;
}
digit[18] = L;
FORR (i, 1, 19) digit[i] = digit[i] - digit[i-1];
REP (i, 19) assert(digit[i] >= 0);
vvi X(3, vi(1));
X[0][0] = A % MOD;
X[1][0] = A % MOD;
X[2][0] = 1;
k = 1;
bool f = true;
REP (i, 19) {
k *= 10;
k %= MOD;
vvi C(3, vi(3));
C[0][0] = k;
C[0][1] = 1;
C[0][2] = B % MOD;
C[1][0] = 0;
C[1][1] = 1;
C[1][2] = B % MOD;
C[2][0] = 0;
C[2][1] = 0;
C[2][2] = 1;
ll n = digit[i];
if (n == 0) continue;
if (f) {
C = pow(C, n-1, MOD);
}
else C = pow(C, n, MOD);
f = false;
X = mult(C, X, MOD);
}
return X[0][0] % MOD;
}
int main() {
cin >> L >> A >> B >> MOD;
cout << solve() << endl;
} |
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#define REP(i,n) for(int i=0;i<n;i++)
#define REPP(i,n) for(int i=1;i<=n;i++)
#define ALL(obj) (obj).begin(), (obj).end()
const double PI = acos(-1);
const double EPS = 1e-15;
long long INF=(long long)1E17;
#define i_7 (long long)(1E9+7)
long mod(long a){
long long c=a%i_7;
if(c>=0)return c;
return c+i_7;
}
using namespace std;
long long po(long long a, long long b, long long m){
if(b==0){
return 1;
}
long long z = po(a,b/2,m);
z = (z*z)%m;
if(b%2!=0){
z = (a*z)%m;
}
return z;
}
bool prime_(int n){
if(n==1){
return false;
}else if(n==2){
return true;
}else{
for(int i=2;i<=sqrt(n);i++){
if(n%i==0){
return false;
}
}
return true;
}
}
long long gcd_(long long a, long long b){
if(a<b){
swap(a,b);
}
if(a%b==0){
return b;
}else{
return gcd_(b,a%b);
}
}
long long lcm_(long long x, long long y){
return (x/gcd_(x,y))*y;
}
int main(){
long long l,a,b,m;
cin>>l>>a>>b>>m;
long long c;
long long power = 1;
long long ans[3];
ans[0] = 0;
ans[1] = a%m;
ans[2] = 1LL;
for(long long d = 1; d<=18; d++){
long long left, right;
left = ((power - a) + b - 1)/b;
left = max(left, 0LL);
right = ((10LL*power - a) + b - 1)/b;
right = min(right, l);
c = right - left;
//cout<<c<<endl;
power *= 10LL;
long long mat[3][3] = {};
mat[0][0] = po(10LL, d, m);
mat[1][0] = mat[1][1] = mat[2][2] = 1LL;
mat[2][1] = b%m;
while(c>0){
if(c & 1){
long long temp[3] = {};
REP(i,3){
REP(j,3){
temp[i] += (ans[j]*mat[j][i])%m;
temp[i] %= m;
}
}
REP(i,3){
ans[i] = temp[i];
}
}
c /= 2;
long long tempMat[3][3] = {};
REP(i,3){
REP(j,3){
REP(k,3){
tempMat[i][j] += (mat[i][k]*mat[k][j])%m;
tempMat[i][j] %= m;
}
}
}
REP(i,3){
REP(j,3){
mat[i][j] = tempMat[i][j];
}
}
}
}
cout<<ans[0]<<endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
int main(){
long long int l, a, b, m;
cin >> l >> a >> b >> m;
vector<long long int> pow10(19, 1);// pow10[i] = 10^i
for(int i=0; i+1<19; i++) pow10[i+1] = pow10[i] * 10;
vector<vector<long long int>> base_matrix(3, vector<long long int>(3));
base_matrix[0][0] = 1;
base_matrix[0][1] = 1;
base_matrix[1][1] = 1;
base_matrix[1][2] = b % m;
base_matrix[2][2] = 1;
bool flag = false;
vector<long long int> ans = {0, (a % m), 1};
for(int d=0; d<18; d++){
if(pow10[d+1] > a+(l-1)*b) flag = true;
base_matrix[0][0] = pow10[d+1] % m;
vector<vector<long long int>> matrix = base_matrix;
long long int c = 0;
if((pow10[d+1]-1) - a >= 0LL) c = (min(a+(l-1)*b, (pow10[d+1]-1)) - a) / b + 1;
if((pow10[d] -1) - a >= 0LL) c -= ((pow10[d]-1) - a) / b + 1;
//cout << c << " ";
for(int b=0; b<60; b++){
if(c >> b & 1){
vector<long long int> memo_ans(3);
for(int i=0; i<3; i++){
for(int j=0; j<3; j++){
memo_ans[i] += (matrix[i][j] * ans[j]) % m;
memo_ans[i] %= m;
}
}
ans = memo_ans;
}
// doubling
vector<vector<long long int>> memo_matrix(3, vector<long long int>(3));
for(int i=0; i<3; i++){
for(int j=0; j<3; j++){
for(int k=0; k<3; k++){
memo_matrix[i][j] += (matrix[i][k] * matrix[k][j]) % m;
memo_matrix[i][j] %= m;
}
}
}
matrix = memo_matrix;
}
if(flag == true) break;
}
cout << ans[0] << endl;
return 0;
} |
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cstdlib>
#include<queue>
#include<set>
#include<cstdio>
using namespace std;
#define ll long long
#define rep(i, n) for(int i = 0; i < n; i++)
#define P pair<int, int>
typedef vector<ll> vec;
typedef vector<vec> mat;
// const ll mod = 1000000007;
mat mat_mul(mat &A, mat &B , ll mod){
mat C(A.size(), vec(B[0].size()));
for (int i = 0; i < A.size(); i++){
for (int k = 0; k < B.size(); k++){
for (int j = 0; j < B[0].size(); j++){
A[i][k] %= mod;
B[k][j] %= mod;
C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % mod;
}
}
}
return C;
}
mat mat_pow(mat A, ll n, ll mod){
mat B(A.size(), vec(A.size()));
for (int i = 0; i < A.size(); i++){
B[i][i] = 1;
}
while(n > 0){
if(n & 1) B = mat_mul(B, A, mod);
A = mat_mul(A, A, mod);
n >>= 1;
}
return B;
}
bool C(ll x, ll ten, ll a, ll b){
ll n = a + b * x;
return n < ten;
}
int main(){
ll L, a, b, m;
cin >> L >> a >> b >> m;
ll x = 0;
ll s = a;
mat X(1, vec(3));
X[0][0] = x; X[0][1] = a; X[0][2] = 1;
ll ten = 1;
ll num_old = -1;
ll num;
rep(i, 18){
ten *= 10;
mat A(3, vec(3));
A[0][0] = ten % m; A[0][1] = 0; A[0][2] = 0;
A[1][0] = 1; A[1][1] = 1; A[1][2] = 0;
A[2][0] = 0; A[2][1] = b % m; A[2][2] = 1;
ll l = -1;
ll r = L - 1;
while(l < r - 1){
ll mid = (l + r) / 2;
if(C(mid, ten, a, b)) l = mid;
else r = mid;
}
if(C(l+1, ten, a, b)) num = l + 1;
else num = l;
ll numd = num - num_old;
num_old = num;
// cout << numd << "abc" << endl;
// cout << A[0][0] << endl;
A = mat_pow(A, numd, m);
// cout << A[0][0] << endl;
X = mat_mul(X, A, m);
// cout << X[0][0] << endl;
}
s = a + (b * (L - 1));
// cout << s << endl;
cout << X[0][0] << endl;
} |
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <iomanip>
#include <cstring>
#include <cmath>
#define pb push_back
#define mk make_pair
#define eps 1e-8
#define fi first
#define se second
#define all(x) (x).begin(),(x).end()
using namespace std;
typedef long long ll;
typedef long double LD;
typedef unsigned int uii;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<int, pair<int, int> >piii;
typedef unsigned long long ull;
typedef vector<int> vii;
typedef vector<ll> vll;
const int inf = 1e9;
const ll INF = 1e18;
// const int M = 1e9 + 7;
//__int128
ll n, a, b, M;
typedef vector<vll> mat;
ll mul(ll x, ll y, ll mod) {
ll ret = 0;
while(y) {
if(y & 1)
ret = (ret + x) % mod;
x = x * 2 % mod;
y >>= 1;
}
return ret;
}
mat mul(mat &A, mat &B){
mat C(A.size(), vll(B[0].size()));
for(int i = 0; i < (int)A.size(); i++){
for(int j = 0; j < (int)B.size(); j++){
for(int k = 0; k < (int)B.size(); k++){
C[i][j] = (C[i][j] + mul(A[i][k], B[k][j], M)) % M;
}
}
}
return C;
}
mat pow(mat A, ll n){
mat B((int)A.size(), vll((int)A.size()));
for(int i = 0; i < (int)A.size(); i++){
B[i][i] = 1;
}
while(n > 0){
if(n & 1) {
B = mul(B, A);
}
A = mul(A, A);
n >>= 1;
}
return B;
}
void test(mat A){
for(int i = 0; i < 3; ++i){
for(int j = 0; j < 3; ++j){
cout << A[i][j] << ' ';
}
cout << endl;
}
}
int main(int argc, char const *argv[])
{
#ifndef ONLINE_JUDGE
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
#endif
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n >> a >> b >> M;
ll base = 1;
ll res = 0;
ll c = 0, last = a - b, tot = 0;
for(int i = 0; i < 19; ++i, base *= 10){
if(base * 10 <= last) continue;
ll step = (base * 10 - last - 1) / b;
if(step + tot >= n){
step = n - tot;
}
if(step == 0) continue;
mat A(3, vll(3));
A[0][1] = A[1][1] = A[1][2] = A[2][2] = 1;
A[0][0] = base * 10;
A = pow(A, step);
res = (mul(res, A[0][0], M) + mul(last + b, A[0][1], M) + mul(b, A[0][2], M)) % M;
// cout << res << endl << endl;
last = last + step * b;
tot += step;
if(tot == n) break;
}
cout << res << endl;
return 0;
} |
#pragma GCC optimize("O2,Ofast,inline,unroll-all-loops,-ffast-math")
#pragma GCC target("popcnt")
#include <bits/stdc++.h>
#define maxn 400010
#define i128 __int128
#define ll long long
#define ull unsigned long long
#define ld long double
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define pob pop_back
#define pf push_front
#define pof pop_front
#define pii pair<int, int>
#define pil pair<int, ll>
#define pll pair<ll, ll>
#define IL inline
#define ss system
using namespace std;
ll p, ans = 0;
struct mat {
ll v[3][3];
mat(int type = 0) {
memset(v, 0, sizeof(v));
if (type) {
for (int i = 0; i < 3; i++) {
v[i][i] = 1;
}
}
}
mat operator * (const mat &rhs) const {
mat ret;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++) {
ret.v[i][j] = (ret.v[i][j] + v[i][k] * rhs.v[k][j]) % p;
}
}
}
return ret;
}
};
i128 n, a, b;
template <class T> void read(T &x) {
char ch = x = 0;
bool fl = false;
while (!isdigit(ch))
fl |= ch == '-', ch = getchar();
while (isdigit(ch))
x = x * 10 + ch - '0', ch = getchar();
x = fl ? -x : x;
}
mat pwm(mat a, i128 b) {
mat ret(1);
while (b) {
if (b & 1)
ret = ret * a;
a = a * a, b >>= 1;
}
return ret;
}
int main() {
read(n), read(a), read(b), cin >> p;
i128 pw = 1;
for (int i = 0; i <= 36; i++, pw *= 10) {
i128 l = pw <= a ? 0 : (pw - a - 1) / b + 1, r = min((pw * 10 - 1 - a) / b, n - 1);
if (pw > a + (n - 1) * b)
break;
if (l > r)
continue;
if (pw * 10 <= a)
continue;
i128 fst = (a % p + l % p * b) % p;
mat base;
base.v[0][1] = base.v[1][1] = base.v[1][2] = base.v[2][2] = 1;
base.v[0][0] = pw * 10 % p;
mat res = pwm(base, r - l + 1);
ans = (ans * res.v[0][0] + fst * res.v[0][1] + b % p * res.v[0][2]) % p;
}
cout << ans << endl;
return 0;
} |
#include <assert.h>
#include <limits.h>
#include <algorithm>
#include <bitset>
#include <cctype>
#include <cmath>
#include <complex>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using ll = long long;
using P = std::pair<ll, ll>;
#define rep(i, a, b) for (ll(i) = (a); i < (b); i++)
#define all(i) i.begin(), i.end()
#define debug(i) std::cerr << "debug "<< i << std::endl
// const ll MOD = 998244353;
const ll MOD = 1e9 + 7;
//非再帰累乗(mod付き)
ll pow_mod(ll a, ll b, ll mod=-1) {
if ((a == 0)||(mod!=-1&&a%mod==0)) {
return 0;
}
ll x = 1;
while (b > 0) {
if (b & 1) {
x = (mod!=-1)?(x * a) % mod:x*a;
}
a = (mod!=-1)?(a * a) % mod:a*a;
b >>= 1;
}
return x;
}
using mat=std::vector<std::vector<ll>>;
mat Mul(mat a,mat b,ll mod){
assert(a[0].size()==b.size());
mat ret(a.size(),std::vector<ll>(b[0].size()));
for(ll i=0;i<a.size();i++){
for(ll j=0;j<b[0].size();j++){
ll temp=0;
for(ll k=0;k<a[0].size();k++){
temp=(temp+a[i][k]*b[k][j])%mod;
}
ret[i][j]=temp;
}
}
return ret;
}
//非再帰累乗(mod付き)
mat pow_mod(mat a, ll b, ll mod=-1) {
ll n=a.size();
mat x(n,std::vector<ll>(n,0));
rep(i,0,n)x[i][i]=1;
while (b > 0) {
if (b & 1) {
x = Mul(x,a,mod);
}
a =Mul(a,a,mod);
b >>= 1;
}
return x;
}
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
//問題文中の添え字が0-indexか1-indexか確認!
ll l,a,b,m;
std::cin>>l>>a>>b>>m;
mat ans(3,std::vector<ll>(1,0));
ans[0][0]=0;ans[1][0]=a%m;ans[2][0]=1;
std::vector<ll> c(19,0);
rep(i,1,19){
ll temp=(pow_mod(10,i)-a-1)/b;
if(temp<0)c[i]=0;
else if(temp<l) c[i]=temp+1;
else c[i]=l;
}
rep(i,1,19){
mat po(3,std::vector<ll>(3,0));
po[0][0]=pow_mod(10,i,m);po[0][1]=1;
po[1][1]=1;po[1][2]=b%m;
po[2][2]=1;
po=pow_mod(po,c[i]-c[i-1],m);
ans=Mul(po,ans,m);
}
std::cout<<ans[0][0];
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int get_length(ll a) {
int res = 0;
for (; a; a/=10) res += 1;
return res;
}
ll find_last_terms(ll a, ll b, ll l, int len) {
ll res = -1;
for (ll lo=0,hi=l-1; lo<=hi; ) {
ll mid = (lo + hi) / 2;
ll ret = get_length(a + b * mid);
if (ret <= len) {
res = max(res, mid);
lo = mid + 1;
} else {
hi = mid - 1;
}
}
return res;
}
ll fast(ll a, ll p, ll mod) {
if (p == 0) return 1;
ll res = fast(a, p >> 1, mod);
res = (res * res) % mod;
if (p & 1) res = (res * a) % mod;
return res;
}
pair<ll,ll> dnc(ll n, ll a, ll b, ll mod, ll len) {
if (n == 0) return make_pair(0, 0);
const ll ONE = fast(10, len, mod);
const ll HALF = fast(ONE, n >> 1, mod);
const ll OFFS = (b * (n / 2)) % mod;
const ll LAST = (a + b * (n-1)) % mod;
pair<ll,ll> res = dnc(n >> 1, a,b,mod, len);
res.first = (
((res.first * HALF) % mod)
+ ((res.first + res.second * OFFS) % mod)
) % mod;
res.second = (res.second * (HALF + 1)) % mod;
if (n & 1) {
res.first = (res.first * ONE + LAST) % mod;
res.second = (res.second * ONE + 1) % mod;
}
return res;
}
int main() {
ll l; scanf("%lld", &l);
ll a,b; scanf("%lld %lld", &a, &b);
ll mod; scanf("%lld", &mod);
int _start = get_length(a);
int _end = get_length(a + b * (l-1));
long long res = 0;
for (int i=_start; i<=_end; i++) {
ll start = find_last_terms(a,b,l,i-1) + 1;
ll end = find_last_terms(a,b,l,i);
const ll SHIFT = fast(fast(10, i, mod), end-start+1, mod);
ll ret = dnc(end-start+1, a + b * start,b,mod, i).first;
res = (res * SHIFT + ret) % mod;
}
printf("%lld\n", res);
return 0;
}
|
#include <iostream>
#include <vector>
#define int long long
#define rep(i, n) for(i = 0; i < n; i++)
using namespace std;
int powmod(int a, int n, int mod) {
if (a >= mod) a %= mod;
if (n == 0) return 1;
if (n % 2 == 0) return powmod((a * a) % mod, n / 2, mod);
return (a * powmod(a, n - 1, mod)) % mod;
}
int p10[19];
int L, a, b, m;
//r^0 + … + r^(n - 1)
int tohi(int r, int n) {
int s[61];
int i;
s[0] = 1;
for (i = 0; i < 60; i++) {
s[i + 1] = s[i] + powmod(r, (1LL << i), m) * s[i];
s[i + 1] %= m;
}
int cnt = 0;
int ret = 0;
for (i = 59; i >= 0; i--) {
if ((n >> i) % 2 == 1) {
ret += powmod(r, cnt, m) * s[i];
ret %= m;
cnt += (1LL << i);
}
}
//cout << "tohi(" << r << ", " << n << ") = " << ret << endl;
return ret;
}
//0 * r^0 + … + (n - 1) * r^(n - 1)
int tohi2(int r, int n) {
int s[61];
int t[61];
int i;
s[0] = 1;
for (i = 0; i < 60; i++) {
s[i + 1] = s[i] + powmod(r, (1LL << i), m) * s[i];
s[i + 1] %= m;
}
t[0] = 0;
for (i = 0; i < 60; i++) {
t[i + 1] = t[i] + powmod(r, (1LL << i), m) * ((1LL << i) % m * s[i] % m + t[i]) % m;
t[i + 1] %= m;
}
int cnt = 0;
int ret = 0;
for (i = 59; i >= 0; i--) {
if ((n >> i) % 2 == 1) {
int res1 = powmod(r, cnt, m);
int res2 = cnt % m * s[i] + t[i]; res2 %= m;
ret += res1 * res2;
ret %= m;
cnt += (1LL << i);
}
}
//cout << "tohi2(" << r << ", " << n << ") = " << ret << endl;
return ret;
}
//a, a + d, …, a + (n - 1)d, x桁
int calc(int a, int d, int n, int x) {
int syu = (a % m + (n - 1) % m * d % m) % m;
int res1 = syu * tohi(p10[x], n) % m;
int res2 = d % m * tohi2(p10[x], n) % m;
return (res1 + m - res2) % m;
}
signed main() {
int i, j;
p10[0] = 1;
for (i = 1; i < 19; i++) p10[i] = p10[i - 1] * 10;
cin >> L >> a >> b >> m;
int ans = 0;
vector<int> cnts;
for (i = 17; i >= 0; i--) {
if (a >= p10[i + 1]) continue;
int l, r; //[l, r]項目はi+1桁
if (a >= p10[i]) { l = 0; }
else { l = (p10[i] - a + b - 1) / b; }
r = (p10[i + 1] - a + b - 1) / b - 1;
if (r >= L) r = L - 1;
if (l > r) continue;
//cout << i << ", " << "[l, r] = " << l << ", " << r << endl;
int syo = a + l * b;
int n = r - l + 1;
int res1 = 1;
rep(j, cnts.size()) {
res1 *= powmod(10, cnts[j], m);
res1 %= m;
}
ans += res1 * calc(syo, b, n, i + 1) % m;
ans %= m;
//cnt += n * (i + 1); <- オーバーフローするのでちょっとズルします。
rep(j, i + 1) cnts.push_back(n);
}
cout << ans << endl;
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcountll
#define INF 1e16
typedef vector<int> vec;
typedef vector<vec> mat;
ll M;
mat operator*(const mat& a,const mat& b){
mat res(3,vec(3,0));
rep(i,3)rep(j,3)rep(k,3){
(res[i][j]+=(a[i][k]%M)*(b[k][j]%M)%M)%=M;
}
return res;
}
mat pow(mat A,ll n){
mat res(3,vec(3,0));
rep(i,3)res[i][i]=1;
while(n>0){
if(n&1)res=res*A;
A=A*A;
n>>=1;
}
return res;
}
int main(){
cin.tie(0);
ios::sync_with_stdio(false);
ll N,A,B;
cin>>N>>B>>A>>M;
ll res=0;
rep(i,18){
ll p1=pow(10LL,i);
ll p2=pow(10LL,i+1);
if(p2<=B||A*(N-1)+B<p1)continue;
ll l=max(0LL,(p1-B+A-1)/A);
ll r=min((p2-B+A-1)/A,N);
mat C(3,vec(3,0));
C[0][0]=1;C[0][1]=A%M;C[0][2]=0;
C[1][0]=0;C[1][1]=1;C[1][2]=0;
C[2][0]=1;C[2][1]=0;C[2][2]=p2%M;
mat D=pow(C,r-l);
ll a=(B+A*l)%M;
res=((a*D[2][0]%M)+D[2][1]+(D[2][2]*res%M))%M;
}
cout<<res<<endl;
return 0;
}
|
#include<bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define all(c) (c).begin(),(c).end()
#define pb push_back
#define dbg(...) do{cerr<<__LINE__<<": ";dbgprint(#__VA_ARGS__, __VA_ARGS__);}while(0);
using namespace std;
namespace std{template<class S,class T>struct hash<pair<S,T>>{size_t operator()(const pair<S,T>&p)const{return ((size_t)1e9+7)*hash<S>()(p.first)+hash<T>()(p.second);}};template<class T>struct hash<vector<T>>{size_t operator()(const vector<T> &v)const{size_t h=0;for(auto i : v)h=h*((size_t)1e9+7)+hash<T>()(i)+1;return h;}};}
template<class T>ostream& operator<<(ostream &os, const vector<T> &v){os<<"[ ";rep(i,v.size())os<<v[i]<<(i==v.size()-1?" ]":", ");return os;}template<class T>ostream& operator<<(ostream &os,const set<T> &v){os<<"{ "; for(const auto &i:v)os<<i<<", ";return os<<"}";}
template<class T,class U>ostream& operator<<(ostream &os,const map<T,U> &v){os<<"{";for(const auto &i:v)os<<" "<<i.first<<": "<<i.second<<",";return os<<"}";}template<class T,class U>ostream& operator<<(ostream &os,const pair<T,U> &p){return os<<"("<<p.first<<", "<<p.second<<")";}
void dbgprint(const string &fmt){cerr<<endl;}template<class H,class... T>void dbgprint(const string &fmt,const H &h,const T&... r){cerr<<fmt.substr(0,fmt.find(","))<<"= "<<h<<" ";dbgprint(fmt.substr(fmt.find(",")+1),r...);}
typedef long long ll;typedef vector<ll> vi;typedef pair<int,int> pi;const int inf = (int)1e9;const double INF = 1e12, EPS = 1e-9;
ll mod;
typedef vector<vi> M;
inline M operator*(const M & a, const M &b){
M c(a.size(), vi(b[0].size()));
rep(i, c.size()) rep(j, c[0].size()){
ll s = 0;
rep(k, a[0].size()) s += (ll)a[i][k] * b[k][j] % mod;
c[i][j] = s % mod;
}
return c;
}
inline M pow(M a, ll m){
M res(a.size(), vi(a.size()));
rep(i, a.size()) res[i][i] = 1;
for(; m; m /= 2){
if(m & 1) res = res * a;
a = a * a;
}
return res;
}
void calc(ll &prev, ll a, ll b, ll n){
ll ten = 1;
for(ll i = a; i; i /= 10) ten = ten * 10 % mod;
M m =
{
{1, 0, 0},
{b, 1, 0},
{0, 1, ten}
};
m = pow(m, n) * M({{1}, {a % mod}, {prev}});
prev = m[2][0];
}
int main(){
cin.tie(0); cin.sync_with_stdio(0);
ll l, a, b; cin >> l >> a >> b >> mod;
ll ans = 0;
while(l){
ll ten = 1;
for(ll i = a; i; i /= 10) ten = ten * 10;
ll m = min((ten - 1 - a) / b, l - 1) + 1;
//dbg(a, b, l, m);
calc(ans, a, b, m);
a = a + b * m;
l -= m;
}
cout << ans << endl;
return 0;
} |
#include <bits/stdc++.h>
using ll = long long;
using namespace std;
long long l, a, b, MOD;
struct Matrix {
vector<vector<long long> > val;
Matrix(int n, int m, long long x = 0) : val(n, vector<long long>(m, x)) {}
void init(int n, int m, long long x = 0) { val.assign(n, vector<long long>(m, x)); }
int size() const { return (int)val.size(); }
inline vector<long long>& operator [] (int i) { return val[i]; }
};
Matrix operator * (Matrix A, Matrix B) {
Matrix R((int)A.size(), (int)B[0].size());
for (int i = 0; i < (int)A.size(); ++i) {
for (int j = 0; j < (int)B[0].size(); ++j) {
for (int k = 0; k < (int)B.size(); ++k) {
R[i][j] = (R[i][j] + A[i][k] * B[k][j] % MOD) % MOD;
}
}
}
return R;
}
Matrix pow(Matrix A, long long n) {
Matrix R((int)A.size(), (int)A.size());
for (int i = 0; i < (int)A.size(); ++i) R[i][i] = 1; // 正方行列
while (n > 0) {
if (n & 1) R = R * A;
A = A * A;
n >>= 1;
}
return R;
}
long long modpow(long long a, long long n) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % MOD;
a = a * a % MOD;
n >>= 1;
}
return res;
}
ll kyu(int n) {
ll res = 0;
for (int i = 0; i < n; i++) res = res * 10 + 9;
return res;
}
Matrix mat(int n) {
Matrix res(3,3);
res[0][0] = modpow(10, n);
res[0][1] = 0;
res[0][2] = 0;
res[1][0] = 1;
res[1][1] = 1;
res[1][2] = 0;
res[2][0] = 0;
res[2][1] = b % MOD;
res[2][2] = 1;
return res;
}
int main() {
cin >> l >> a >> b >> MOD;
Matrix data(1,3);
data[0][0] = 0;
data[0][1] = a % MOD;
data[0][2] = 1;
for (int i = 1; i <= 18; i++) {
ll from = kyu(i-1), to = kyu(i);
from = ( from - a < 0 ? -1 : (from - a) / b );
to = ( to - a < 0 ? -1 : (to - a) / b );
if (from >= l - 1) break;
if (to < 0) continue;
if (to >= l - 1) to = l - 1;
ll count = to - from;
data = data * pow(mat(i), count);
}
cout << data[0][0] % MOD << endl;
return 0;
} |
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#define mkp make_pair
typedef long long ll;
using namespace std;
ll L,A,B,M;
ll d[20];
ll MOD=1000000007;
typedef vector<ll> vec;//ll?
typedef vector<vec> mat;
mat mul(mat &A,mat &B){
mat C(A.size(),vec(B[0].size()));
for(int i=0;i<A.size();i++){
for(int k=0;k<B.size();k++){
for(int j=0;j<B[0].size();j++){
C[i][j]=(C[i][j]+A[i][k]*B[k][j]%MOD)%MOD;
}
}
}
return C;
}
mat pow(mat A,ll n){
mat B(A.size(),vec(A.size()));
for(int i=0;i<A.size();i++){
B[i][i]=1;
}
while(n>0){
if(n&1) B=mul(B,A);
A=mul(A,A);
n=(n>>1);
}
return B;
}
int digit(ll val){
if(val==0) return 0;
else return (1+digit(val/10));
}
int main(){
cin>>L>>A>>B>>M;
MOD=M;
ll ans=0;
ll s=A;
ll ten[20]={};
ten[0]=1;
for(int i=1;i<=18;i++) ten[i]=ten[i-1]*10%MOD;
ll start=0;
while(start<L){
ll ng=L;
ll ok=start;
ll nowdigit=digit(A+B*start);
while(ng-ok>1){
ll mid=(ng+ok)/2;
if(digit(A+B*mid)==nowdigit) ok=mid;
else ng=mid;
}
mat C(3,vec(3));
C[0][0]=ten[nowdigit];
C[0][1]=1;
C[0][2]=0;
C[1][0]=0;
C[1][1]=1;
C[1][2]=B%MOD;
C[2][0]=0;
C[2][1]=0;
C[2][2]=1;
C=pow(C,(ok-start+1));
mat D(3,vec(1));
D[0][0]=ans;
D[1][0]=(A+B*start)%MOD;
D[2][0]=1;
D=mul(C,D);
ans=D[0][0];
ans=(ans+MOD)%MOD;
start=ok+1;
}
cout<<ans<<endl;
return 0;
}
|
#include <bits/stdc++.h>
#define ll long long
using namespace std;
inline ll read() {
ll x = 0, f = 1; char ch = getchar();
while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); }
while (ch >= '0' && ch <= '9') { x = x * 10 + ch - 48; ch = getchar(); }
return x * f;
}
ll mod;
struct M { ll a[3][3]; };
M operator * (const M &a, const M &b) {
M c;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
c.a[i][j] = 0;
for (int k = 0; k < 3; k++) {
c.a[i][j] = (c.a[i][j] + a.a[i][k] * b.a[k][j] % mod) % mod;
}
}
}
return c;
}
M qp(M a, ll b) {
M c;
for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) c.a[i][j] = i == j;
while (b) {
if (b & 1) c = c * a;
a = a * a;
b >>= 1;
}
return c;
}
int main() {
ll n = read(), a0 = read(), d = read(); mod = read();
n--;
ll bit = 10, ans = 0;
ll st = 0;
for (int i = 1; i <= 19; i++) {
ll l = st, r = n, p = -1;
while (l <= r) {
ll mid = l + r >> 1;
if (mid * d + a0 < bit) l = mid + 1, p = mid;
else r = mid - 1;
}
if (p != -1) {
M a;
a.a[0][0] = bit % mod; a.a[0][1] = a.a[1][1] = a.a[2][2] = 1LL;
a.a[0][2] = a.a[1][0] = a.a[2][0] = a.a[2][1] = 0LL;
a.a[1][2] = d % mod;
a = qp(a, p - st + 1);
ll ast = a0 % mod + d % mod * st % mod; ast %= mod;
ans = (ans * a.a[0][0] % mod + ast * a.a[0][1] % mod + a.a[0][2] % mod) % mod;
st = p + 1;
}
if (st > n) break;
bit *= 10;
}
printf("%lld\n", ans);
return 0;
} |
#include <bits/stdc++.h>
using namespace std;
using int128_t = __int128_t;
int128_t MOD;
void add(int128_t& a, int128_t b){
a = (a+b) % MOD;
}
void mul(int128_t& a, int128_t b){
a = a*b % MOD;
}
int dig(int128_t n){
int d = 1;
int128_t prod = 1;
while(prod*10 <= n){
d++;
prod *= 10;
}
return d;
}
int128_t power_mod(int128_t num, int128_t power){
int128_t prod = 1;
num %= MOD;
while(power > 0){
if(power&1) prod = prod * num % MOD;
num = num * num % MOD;
power >>= 1;
}
return prod;
}
map<int128_t, int128_t> mpT, mpS;
int128_t T(int128_t r, int128_t N){
if(N == 0) return 0;
if(mpT.count(N)) return mpT[N];
int128_t res;
if(N%2){
res = 1 + r*(T(r, N-1));
}else{
res = (1 + power_mod(r, N/2)) * T(r, N/2);
}
res %= MOD;
mpT[N] = res;
return res;
}
int128_t S(int128_t r, int128_t N){
if(N == 0) return 0;
if(mpS.count(N)) return mpS[N];
int128_t res;
if(N%2){
res = S(r, N-1) + N*power_mod(r, N-1);
}else{
res = S(r, N/2) + power_mod(r, N/2)*((N/2)*T(r, N/2) + S(r, N/2));
}
res %= MOD;
mpS[N] = res;
return res;
}
int128_t calc_T(int128_t r, int128_t N){
mpT.clear();
return T(r, N);
}
int128_t calc_S(int128_t r, int128_t N){
mpT.clear();
mpS.clear();
return S(r, N);
}
int main(){
int64_t tmp1, tmp2, tmp3, tmp4;
cin >> tmp1 >> tmp2 >> tmp3 >> tmp4;
int128_t L = tmp1, A = tmp2, B = tmp3;
MOD = tmp4;
int D = dig(A+B*(L-1));
int64_t last = L-1;
int128_t ans = 0, base = 1;
for(int d=D; d>=dig(A); d--){
if(dig(A+B*last) != d) continue;
int64_t ok = last, ng = -1;
while(ok-ng>1){
int128_t mid = (ok+ng)/2;
(dig(A + B*mid) == d ? ok : ng) = mid;
}
int128_t N = last-ok+1;
int128_t res = (A + (last+1)*B) % MOD * calc_T(power_mod(10, d), N) % MOD;
int128_t sub = B * calc_S(power_mod(10, d), N) % MOD;
add(res, MOD - sub);
add(ans, res*base);
mul(base, power_mod(10, N*d));
last = ok-1;
}
int64_t Ans = ans;
cout << Ans << endl;
return 0;
}
|
#include <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;
typedef vector<ll>vec;
typedef vector<vec>mat;
ll L,A,B,MOD;
mat mul(mat&a, mat&b) {
mat c(a.size(), vec(b[0].size()));
rep(i, a.size())rep(j, b[0].size())rep(k, b.size())
(c[i][j] += a[i][k] * b[k][j]) %= MOD;
return c;
}
mat ppow(mat&a, ll b) {
mat res(a.size(), vec(a.size()));
rep(i, a.size())res[i][i] = 1;
while (b) {
if (b & 1)res = mul(res, a);
a = mul(a, a);
b >>= 1;
}
return res;
}
ll ppow(ll a,ll b){
a%=MOD;
ll res=1;
while(b){
if(b&1)res=(res*a)%MOD;
a=(a*a)%MOD;
b>>=1;
}
return res;
}
ll lb(ll x){
ll ok=L,ng=-1;
while(ok-ng>1){
ll t=(ok+ng)/2;
if(A+B*t>=x)ok=t;
else ng=t;
}
return ok;
}
int main(){
cin>>L>>A>>B>>MOD;
ll d=1;
ll ans=0;
for(ll i=1;i<=18;i++){
ll l=lb(d),r=lb(d*10);
(ans*=ppow(d*10,(r-l)))%=MOD;
ll s=(A+B%MOD*l)%MOD;
mat M1{{d*10%MOD,1,0},{0,1,1},{0,0,1}};
mat M2{{0},{s},{B%MOD}};
mat res=ppow(M1,r-l);
M2=mul(res,M2);
(ans+=M2[0][0])%=MOD;
d*=10;
}
cout<<ans<<endl;
} |
#include<iostream>
using namespace std;
long L,A,B,M;
long power(long a,long b){return b?power(a*a%M,b/2)*(b%2?a:1)%M:1;}
long ten[99],sten[99],iten[99];
long n;
long sum(long k)
{
long ret=0,p=1;
for(int i=61;i--;)
{
if(k>>i&1)
{
(ret+=sten[i]*p)%=M;
p=p*ten[i]%M;
}
}
return ret;
}
long isum(long k)
{
long ret=0,p=1,g=0;
for(int i=61;i--;)
{
if(k>>i&1)
{
(ret+=(iten[i]+sten[i]*g)%M*p)%=M;
p=p*ten[i]%M;
g=(g+(1LL<<i))%M;
}
}
return ret;
}
long cnt[18],SUM[18];
int main()
{
cin>>L>>A>>B>>M;
long pre=-1,tmpten=1;
long ans=0;
for(n=1;n<=18;n++)
{
cnt[n-1]=1;
long l=pre,r=L;
tmpten*=10;
while(r-l>1)
{
long m=(l+r)/2;
if(A+B*m<tmpten)l=m;
else r=m;
}
long k=l-pre;
if(k<0)
{
continue;
}
pre=l;
ten[0]=tmpten%M;
sten[0]=1;
iten[0]=0;
if(k&1)cnt[n-1]=tmpten%M;
for(int i=1;i<61;i++)
{
ten[i]=ten[i-1]*ten[i-1]%M;
sten[i]=(ten[i-1]+1)%M*sten[i-1]%M;
iten[i]=((ten[i-1]+1)%M*iten[i-1]+(1LL<<i-1)%M*sten[i-1]%M*ten[i-1])%M;
if(k>>i&1)cnt[n-1]=cnt[n-1]*ten[i]%M;
}
long ret=0,p=1;
for(int i=61;i--;)
{
if(k>>i&1)
{
(ret+=sten[i]*p)%=M;
p=p*ten[i]%M;
}
}
SUM[n-1]=(A+B*l)%M*ret%M;
ret=0;
p=1;
long g=0;
for(int i=61;i--;)
{
if(k>>i&1)
{
(ret+=(iten[i]+sten[i]*g)%M*p)%=M;
p=p*ten[i]%M;
g=(g+(1LL<<i))%M;
}
}
SUM[n-1]=((SUM[n-1]-B%M*ret)%M+M)%M;
}
long p=1;
for(int i=18;i--;)
{
ans=(ans+SUM[i]*p)%M;
p=p*cnt[i]%M;
}
cout<<ans<<endl;
}
|
#include<iostream>
#include<iomanip>
#include<vector>
#include<string>
#include<cstring>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<algorithm>
#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<climits>
#include<fstream>
//#define MOD (1000000007)
using namespace std;
typedef long long int Int;
constexpr Int TEN(int n) { return n == 0 ? 1 : 10 * TEN(n-1); }
Int mod;
Int L,A,B;
typedef struct M {
Int data[3][3];
}Matrix;
Matrix create(Int op, Int b) {
Matrix a;
a.data[0][0] = op%mod;
a.data[0][1] = a.data[0][2] = 0;
a.data[1][0] = 1;
a.data[1][1] = 1;
a.data[1][2] = 0;
a.data[2][0] = 0;
a.data[2][1] = b%mod;
a.data[2][2] = 1;
return a;
}
Matrix operator * (Matrix a, Matrix b) {
Matrix c;
for(int i = 0;i < 3;i++) {
for(int j = 0;j < 3;j++) {
c.data[i][j] = 0;
for(int k = 0;k < 3;k++) {
c.data[i][j] += (a.data[i][k]*b.data[k][j])%mod;
c.data[i][j] %= mod;
}
}
}
return c;
}
Matrix pow(Matrix a, Int n) {
if(n == 0) {
Matrix d;
for(int i = 0;i < 3;i++) {
for(int j = 0;j < 3;j++) {
d.data[i][j] = 0;
}
}
d.data[0][0] = d.data[1][1] = d.data[2][2] = 1;
return d;
}
Matrix ret;
ret = pow(a*a, n/2);
if(n&1)
ret = ret*a;
return ret;
}
int main(void) {
cin>>L>>A>>B>>mod;
Int prev = 0;
Int op = 10;
Int X = 0;
L--;
for(int d = 1;d < 19;d++) { //digit
Int l = prev;
Int r = L;
Int curr = -1;
while(l <= r) {
Int mid = (l+r)/2;
Int c = A+B*mid;
if(c < op) {
curr = mid;
l = mid+1;
} else {
r = mid-1;
}
}
if(curr != -1) {
Matrix M = create(op,B);
M = pow(M, curr+1-prev);
Int s = (A+B*prev%mod)%mod;
X = (X*M.data[0][0]%mod+s*M.data[1][0]%mod+M.data[2][0])%mod;
prev = curr+1;
}
op *= 10;
}
cout<<X<<endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
template <typename T>
struct Matrix {
vector<vector<T>> mat;
Matrix(int n, int m, T val = 0) : mat(n, vector<long long>(m, val)) {};
void init(int n, int m, T val = 0) {mat.assigin(n, vector<long long>(m, val));}
size_t size() const {return mat.size();}
inline vector<long long>& operator[](int i) {return mat[i];}
};
long long MOD;
template <typename T>
Matrix<T> operator*(Matrix<T> A, Matrix<T> B) {
Matrix<T> C(A.size(), B[0].size());
for(int i = 0; i < A.size(); ++i) {
for(int j = 0; j < B[0].size(); ++j) {
for(int k = 0; k < B.size(); ++k) {
C[i][j] = (C[i][j] + A[i][k] * B[k][j] % MOD) % MOD;
}
}
}
return C;
}
template <typename T>
Matrix<T> pow(Matrix<T> A, long long n) {
Matrix<T> C(A.size(), A.size());
for(int i = 0; i < A.size(); ++i) C[i][i] = 1;
while(n > 0) {
if(n & 1) C = C * A;
A = A * A;
n >>= 1;
}
return C;
}
using mat = Matrix<long long>;
using vec = vector<long long>;
vec pro(mat A, vec X, long long C){
vec ret(3, 0);
mat Apro = pow(A, C);
for(int i=0; i<3; ++i) {
for(int j=0; j<3; ++j) {
ret[i] = (ret[i] + Apro[i][j] * X[j] % MOD) % MOD;
}
}
return ret;
}
long long powmod(long long x, long long n) {
long long ret = 1;
while(n > 0) {
if(n & 1) ret = ret * x % MOD;
x = x * x % MOD;
n >>= 1;
}
return ret;
}
int main() {
long long L, A, B;
cin >> L >> A >> B >> MOD;
int start = 0;
long long tmp = 1;
for(; start < 18; ++start) {
if(A >= tmp && A < tmp * 10) break;
tmp *= 10;
}
vec C(18);
long long prev = A - B, cnt = 0;
for(int i=start; i<18; ++i) {
C[i] = ((long long)pow(10, i + 1) - prev) / B;
if(prev + B * C[i] == (long long)pow(10, i + 1)) --C[i];
C[i] = min(C[i], L - cnt);
cnt += C[i];
if(cnt == L) break;
prev += B * C[i];
}
vec X = {0, A, B};
mat coeff(3, 3);
coeff[0] = {1, 1, 0};
coeff[1] = {0, 1, 1};
coeff[2] = {0, 0, 1};
for(int d=0; d<18; ++d) {
coeff[0][0] = powmod(10, d + 1);
X = pro(coeff, X, C[d]);
}
cout << X[0] % MOD << endl;
} |
#include <bits/stdc++.h>
#define sz(c) int(c.size())
#define rep(i,a,b) for (int i=a; i<(b); ++i)
#define per(i,a,b) for (int i=(b)-1; i>=(a); --i)
using namespace std;
using ll = long long;
int M;
inline int madd(int x,int y) {
if (x+y<M) return x+y; else return x+y-M;
}
inline int msub(int x,int y) {
if (x-y>=0) return x-y; else return x-y+M;
}
inline int mmul(int x,int y) {
return int(ll(x)*y % M);
}
template<class T,int N,int P,int M>
void matmul(T res[][M], const T A[][P], const T B[][M]) { // res[NxM] = A[NxP] * B[PxM]
static T tmp[N][M];
rep(i,0,N) rep(j,0,M) tmp[i][j]=0;
rep(i,0,N) rep(j,0,M) rep(k,0,P) {
tmp[i][j]=madd(tmp[i][j],mmul(A[i][k],B[k][j]));
}
rep(i,0,N) rep(j,0,M) res[i][j]=tmp[i][j];
}
template<class T,int N>
void matpow(T res[][N], const T A[][N], ll p) { // res[1xN] *= A[NxN]^p
static T tmp[N][N];
rep(i,0,N) rep(j,0,N) tmp[i][j]=A[i][j];
while (p>0) {
if (p%2) matmul<T,1>(res,res,tmp);
matmul<T,N>(tmp,tmp,tmp);
p/=2;
}
}
int len(ll x) {
assert(x>0);
int res=0;
while (x>0) {
x/=10;
res++;
}
return res;
}
ll find_len(ll L,ll A,ll B) {
int z=len(A);
ll l=0,r=L;
while (l<r) {
ll m=l+(r-l)/2;
if (z==len(A+B*m)) l=m+1; else r=m;
}
return l;
}
int main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
cout<<fixed<<setprecision(10);
ll L,A,B;
cin>>L>>A>>B>>M;
int sum=0;
while (L>0) {
ll k=find_len(L,A,B);
int p=1;
rep(i,0,len(A)) p=mmul(p,10);
int r[1][3]={{sum,int(A%M),1}};
int X[3][3]={{p,0,0},
{1,1,0},
{0,int(B%M),1}};
matpow(r,X,k);
sum=r[0][0];
L-=k;
A+=B*k;
}
cout<<sum<<"\n";
}
|
#include <bits/stdc++.h>
using namespace std;
//F
long long l,a,b,mod,d[20]={0},c;
int i;
long long powmod(long long x, long long y){
if(y==0) return 1;
else if(y%2==0) return powmod((x*x)%mod,y/2);
else return (powmod(x,y-1)*x)%mod;
}
long long mypow(long long x, long long y){
if(y==0) return 1;
else if(y%2==0) return mypow((x*x),y/2);
else return (mypow(x,y-1)*x);
}
array<long long,9> matprod(array<long long,9> p,array<long long,9> q){
array<long long,9> r;
r[0]=(p[0]*q[0]%mod+p[1]*q[3]%mod+p[2]*q[6]%mod)%mod;
r[1]=(p[0]*q[1]%mod+p[1]*q[4]%mod+p[2]*q[7]%mod)%mod;
r[2]=(p[0]*q[2]%mod+p[1]*q[5]%mod+p[2]*q[8]%mod)%mod;
r[3]=(p[3]*q[0]%mod+p[4]*q[3]%mod+p[5]*q[6]%mod)%mod;
r[4]=(p[3]*q[1]%mod+p[4]*q[4]%mod+p[5]*q[7]%mod)%mod;
r[5]=(p[3]*q[2]%mod+p[4]*q[5]%mod+p[5]*q[8]%mod)%mod;
r[6]=(p[6]*q[0]%mod+p[7]*q[3]%mod+p[8]*q[6]%mod)%mod;
r[7]=(p[6]*q[1]%mod+p[7]*q[4]%mod+p[8]*q[7]%mod)%mod;
r[8]=(p[6]*q[2]%mod+p[7]*q[5]%mod+p[8]*q[8]%mod)%mod;
return r;
}
array<long long,9> matpow(array<long long,9> p,long long x){
if(x==0) return {1,0,0,0,1,0,0,0,1};
if(x%2==0) return matpow(matprod(p,p),x/2);
else return matprod(matpow(p,x-1),p);
}
int main() {
// your code goes here
cin >> l >> a >> b >> mod;
for(i=1;i<=18;i++){
if(mypow(10,i)<a) d[i]=0;
else{
d[i]=((mypow(10,i)-1-a)-(mypow(10,i)-1-a)%b)/b+1;
}
d[i]=min(d[i],l);
}
array<long long,9> ans={1,0,0,0,1,0,0,0,1},mx;
for(i=1;i<=18;i++){
c=d[i]-min(d[i],d[i-1]);
mx={powmod(10,i),0,0,1,1,0,0,b%mod,1};
ans=matprod(ans,matpow(mx,c));
}
mx={0,a%mod,1,0,0,0,0,0,0};
ans=matprod(mx,ans);
cout << ans[0] << endl;
return 0;
} |
#include <bits/stdc++.h>
using i64 = long long;
using Mat = std::vector<std::vector<i64>>;
i64 mod;
Mat operator*(const Mat &lhs, const Mat &rhs) {
int n = lhs.size();
Mat ret(n, std::vector<i64>(n));
for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) for (int k = 0; k < n; k++) {
ret[i][j] = (ret[i][j] + lhs[i][k] * rhs[k][j] % mod) % mod;
}
return ret;
}
Mat pow(Mat m, i64 k) {
const int size = m.size();
Mat ret(size, std::vector<i64>(size));
for (int i = 0; i < size; i++) ret[i][i] = 1;
while (k) {
if ((k & 1) == 1) ret = m * ret;
m = m * m;
k >>= 1ll;
}
return ret;
}
int main() {
i64 n, a, b;
std::cin >> n >> a >> b >> mod;
std::vector<i64> dcnt(20);
i64 sum = 0;
int initial = std::to_string(a).length();
for (i64 i = initial; i < 20; i++) {
i64 l = 0, r = n, th = 1;
for (i64 j = 0; j < i; j++) th *= 10;
while (r - l > 1) {
i64 k = (l + r) / 2;
i64 s = a + b * k;
if (s < th) l = k;
else r = k;
}
dcnt[i] = l + 1 - sum;
sum = l + 1;
}
i64 dd = 10;
i64 ret = 0, s = a;
for (i64 i = 1; i <= 18; i++) {
Mat m { { dd, 0, 0 }, { 1, 1, 0 }, { 0, b, 1 } };
m = pow(m, dcnt[i]);
ret = (ret * m[0][0] % mod + s * m[1][0] % mod + m[2][0]) % mod;
s = (s * m[1][1] % mod + m[2][1]) % mod;
dd = dd * 10 % mod;
}
std::cout << ret << std::endl;
return 0;
}
|
#include <bits/stdc++.h>
using namespace std;
using Int = long long;
Int powmod(Int x, unsigned long long y, Int M)
{
if (y == 0) return 1;
if (y % 2 == 0) return powmod(x*x%M, y/2, M);
return x*powmod(x*x%M, y/2, M)%M;
}
Int f(Int A, Int B, Int R, Int N, Int M)
{
if (N == 0) return 0;
if (N % 2 == 0) return f((A*R+A+B)%M, 2*(B+R*B)%M, R*R%M, N/2, M);
return (f(A, B, R, N-1, M)*R + (N-1)%M*B%M+A)%M;
}
int main()
{
Int L, A, B, M; cin >> L >> A >> B >> M;
array<Int, 19> counts = {};
Int idx = 0;
for (int i = 1; i < counts.size(); i++) {
Int k = (Int)pow(10, i) - 1 - A;
if (k < idx*B) continue;
k /= B;
k = min(L-1, k);
counts[i] = k - idx + 1;
idx += counts[i];
}
Int ans = 0;
for (int i = 1; i < counts.size(); i++) {
unsigned long long s = 0, t = 0;
for (int j = 1; j < i; j++) s += counts[j];
for (int j = i+1; j < counts.size(); j++) t += j * counts[j];
ans = (ans + f((A%M+B%M*(s%M))%M, B%M, powmod(10, i, M), counts[i], M) * powmod(10, t, M)) % M;
}
cout << ans << '\n';
return 0;
}
|
#include <bits/stdc++.h>
#define ll long long
using namespace std;
inline ll read() {
ll x = 0, f = 1; char ch = getchar();
while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); }
while (ch >= '0' && ch <= '9') { x = x * 10 + ch - 48; ch = getchar(); }
return x * f;
}
ll mod;
struct M { ll a[3][3]; };
M operator * (const M &a, const M &b) {
M c;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
c.a[i][j] = 0;
for (int k = 0; k < 3; k++) {
c.a[i][j] = (c.a[i][j] + a.a[i][k] * b.a[k][j] % mod) % mod;
}
}
}
return c;
}
M qp(M a, ll b) {
M c;
for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) c.a[i][j] = i == j;
while (b) {
if (b & 1) c = c * a;
a = a * a;
b >>= 1;
}
return c;
}
int main() {
ll n = read(), a0 = read(), d = read(); mod = read();
ll bit = 10, ans = 0;
ll st = 0;
for (int i = 1; i <= 19; i++) {
ll l = st, r = n, p = -1;
while (l + 1 < r) {
ll mid = l + r >> 1;
if (mid * d + a0 < bit) l = mid , p = mid;
else r = mid;
}
if (l * d + a0 < bit) p = l;
if (p != -1) {
M a;
a.a[0][0] = bit % mod; a.a[0][1] = a.a[1][1] = a.a[2][2] = 1LL;
a.a[0][2] = a.a[1][0] = a.a[2][0] = a.a[2][1] = 0LL;
a.a[1][2] = d % mod;
a = qp(a, p - st + 1);
ll ast = a0 % mod + d % mod * st % mod; ast %= mod;
ans = (ans * a.a[0][0] % mod + ast * a.a[0][1] % mod + a.a[0][2] % mod) % mod;
st = p + 1;
}
if (st >= n) break;
bit *= 10;
}
printf("%lld\n", ans);
return 0;
} |
#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < n; ++i)
using namespace std;
typedef long long ll;
int mod;
struct mint {
ll x;
mint(ll x=0):x(x%mod){}
mint& operator+=(const mint a) {
(x += a.x) %= mod;
return *this;
}
mint& operator-=(const mint a) {
(x += mod-a.x) %= mod;
return *this;
}
mint& operator*=(const mint a) {
(x *= a.x) %= mod;
return *this;
}
mint operator+(const mint a) const {
mint res(*this);
return res+=a;
}
mint operator-(const mint a) const {
mint res(*this);
return res-=a;
}
mint operator*(const mint a) const {
mint res(*this);
return res*=a;
}
};
ll b, ten;
mint pow_(mint x, ll t) {
if (t == 0) return 1;
if (t%2 == 1) {
return pow_(x,t-1)*x;
} else {
mint y = pow_(x,t/2);
return y*y;
}
}
mint f(ll l) {
if (l == 0) return 0;
if (l%2 == 1) {
ll pl = l-1;
mint x = f(pl);
return x*ten + 1;
} else {
ll pl = l/2;
mint x = f(pl);
return x*pow_(ten, pl) + x;
}
}
mint g(ll l) {
if (l == 0) return 0;
if (l%2 == 1) {
ll pl = l-1;
mint x = g(pl);
return x*ten + mint(b)*pl;
} else {
ll pl = l/2;
mint x = g(pl);
return x*pow_(ten, pl) + x + mint(b)*pl*f(pl);
}
}
int main() {
ll L, a;
cin >> L >> a >> b >> mod;
ll last = a+b*(L-1);
mint ans = 0;
ten = 10;
for (int i = 1; i <= 18; ++i, ten *= 10) {
ll l = ten/10, r = ten-1;
if (last < l) continue;
if (a > r) continue;
ll na = 0; // 初項
ll nl = 0; // 長さ
{
if (a >= l) na = a;
else {
na = ((l-a)+(b-1))/b*b+a;
na = min(na, last);
}
}
{
ll nlast = 0;
if (last <= r) nlast = last;
else {
nlast = (r-a)/b*b+a;
}
nl = (nlast-na)/b+1;
}
// cerr << i << ' ' << na << " " << nl << endl;
ans *= pow_(ten, nl);
ans += f(nl)*na;
ans += g(nl);
// cerr << f(nl).x << endl;
// cerr << g(nl).x << endl;
// cerr << ans.x << endl;
}
cout << ans.x << endl;
return 0;
}
|
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
const int INF = (1<<30);
const ll INFLL = (1ll<<60);
const ll MOD = (ll)(1e9+7);
#define l_ength size
void mul_mod(ll& a, ll b){
a *= b;
a %= MOD;
}
void add_mod(ll& a, ll b){
a = (a<MOD)?a:(a-MOD);
b = (b<MOD)?b:(b-MOD);
a += b;
a = (a<MOD)?a:(a-MOD);
}
ll c[20],d[20]={1ll},r[20]={1ll},m,ans[1][3],mt[3][3],tmp[3][3];
void mul1(){
int i,j,k;
for(i=0; i<1; ++i){
for(j=0; j<3; ++j){
for(k=0; k<3; ++k){
tmp[i][j] += (ans[i][k]*mt[k][j])%m;
tmp[i][j] %= m;
}
}
}
for(i=0; i<1; ++i){
for(j=0; j<3; ++j){
ans[i][j] = tmp[i][j];
tmp[i][j] = 0ll;
}
}
}
void mul2(){
int i,j,k;
for(i=0; i<3; ++i){
for(j=0; j<3; ++j){
for(k=0; k<3; ++k){
tmp[i][j] += (mt[i][k]*mt[k][j])%m;
tmp[i][j] %= m;
}
}
}
for(i=0; i<3; ++i){
for(j=0; j<3; ++j){
mt[i][j] = tmp[i][j];
tmp[i][j] = 0ll;
}
}
}
int main(void){
int i;
ll l,a,b,q;
cin >> l >> a >> b >> m;
ans[0][0] = 0ll; ans[0][1] = a%m; ans[0][2] = 1ll;
for(i=0; i<18; ++i){
d[i+1] = d[i]*10;
r[i+1] = r[i]*10;
r[i+1] %= m;
}
c[0] = -1ll;
for(i=1; i<=18; ++i){
--d[i];
if(a>d[i]){
c[i] = -1ll;
continue;
}else{
c[i] = min((d[i]-a)/b,l-1);
}
}
for(i=1; i<=18; ++i){
if(a>d[i]){
continue;
}
q = c[i]-c[i-1];
mt[0][0] = r[i]; mt[0][1] = 0ll; mt[0][2] = 0ll;
mt[1][0] = 1ll; mt[1][1] = 1ll; mt[1][2] = 0ll;
mt[2][0] = 0ll; mt[2][1] = b%m; mt[2][2] = 1ll;
while(q){
if(q&1){
mul1();
}
mul2();
q /= 2;
}
}
cout << ans[0][0] << endl;
return 0;
}
|
#include<bits/stdc++.h>
//ios::sync_with_stdio(false);
//cin.tie(0);
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<pii,int> ppii;
typedef pair<int,pii> pipi;
typedef pair<ll,ll> pll;
typedef pair<pll,ll> ppll;
typedef pair<ll,pll> plpl;
typedef tuple<ll,ll,ll> tl;
ll mod=1000000007;
ll mod2=998244353;
ll inf=1000000000000000000;
double pi=2*acos(0);
#define rep(i,m,n) for(int i=m;i<n;i++)
#define rrep(i,n,m) for(int i=n;i>=m;i--)
int dh[4]={1,-1,0,0};
int dw[4]={0,0,1,-1};
int ddh[8]={-1,-1,-1,0,0,1,1,1};
int ddw[8]={-1,0,1,-1,1,-1,0,1};
ll lmax(ll a,ll b){
if(a<b)return b;
else return a;
}
ll lmin(ll a,ll b){
if(a<b)return a;
else return b;
}
ll m;
vector<vector<ll>> matmul(vector<vector<ll>> a,vector<vector<ll>> b){
ll n=a.size();
vector<vector<ll>> ret;
vector<ll> e;
rep(i,0,n)e.push_back(0);
rep(i,0,n)ret.push_back(e);
rep(i,0,n){
rep(j,0,n){
ll sum=0;
rep(k,0,n){
sum+=(a[i][k]*b[k][j])%m;
sum%=m;
}
ret[i][j]=sum;
}
}
return ret;
}
vector<vector<ll>> matbeki(vector<vector<ll>> a,ll n){
vector<vector<ll>> ret;
ll m=a.size();
vector<ll> e;
rep(i,0,m)e.push_back(0);
rep(i,0,m)ret.push_back(e);
rep(i,0,m){
rep(j,0,m){
if(i==j)ret[i][j]=1;
else ret[i][j]=0;
}
}
while(n>0){
if(n%2){
ret=matmul(ret,a);
}
a=matmul(a,a);
n/=2;
}
return ret;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
ll l,a,b;cin>>l>>a>>b>>m;
ll now=1;
for(;;){
if(now>a)break;
now*=10;
}
ll usi=0;
ll ans=0;
ll r=a;
for(;;){
ll u=(now-a)/b;
if((now-a)%b!=0)u++;
u=min(u,l);
vector<vector<ll>> v={{now%m,1,0},{0,1,1},{0,0,1}};
vector<vector<ll>> w=matbeki(v,u-usi);
ll rr=r%m;
ll bb=b%m;
ll y=(ans*w[0][0])%m;
ll e=(w[0][1]*rr)%m;
ll ee=(w[0][2]*bb)%m;
y+=e+ee;
y%=m;
ans=y;
usi=u;
r=b*u+a;
now*=10;
//cout<<ans<<" "<<u<<" "<<now<<" "<<r<<endl;
if(u==l)break;
}
cout<<ans<<endl;
}
|
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
ll L, A, B, M, AM, BM;
struct finfo {
ll rmul;
ll amul;
ll c;
};
finfo fi[100];
/*
ダブリング
fi[i] : f(r,a,2^i)の係数を計算する
f(r,a,2^i,k) = fi[i].rmul*r + fi[i].amul*a + fi[i].c +
2^i = n とする
i-1 = j
2^j = m とする
fi[i].rmul -> rn
fi[i].amul -> an
fi[i].cmul -> cn
fi[j].rmul -> rm
fi[j].amul -> am
fi[j].cmul -> cm
f(r,a,m) = rm*r + am*a + cm
f(r,a,2*m) = f(f(r,a,m),a+m*B,m)
= f((rm*r + am*a + cm),a+m*B,m)
= rm*(rm*r + am*a + cm) + am*(a+m*B) + cm
= r * (rm*rm)
+ a * (rm*am+am)
+ rm*cm+cm + am*m*B
*/
void calc_fi( ll r, ll a, ll keta, ll k ){
fi[0] = { k%M, 1, 0 };
ll m = 1;
for ( int i = 1; i < 64; i++ ){
fi[i].rmul = (fi[i-1].rmul * fi[i-1].rmul)%M;
fi[i].amul = ((fi[i-1].rmul+1)*fi[i-1].amul)%M;
fi[i].c = ((fi[i-1].rmul+1)*fi[i-1].c%M + (((fi[i-1].amul*m)%M)*BM)%M)%M;
m = (m*2)%M;
}
//cout << "calc" << k << endl;
//for ( int i = 0; i < 10; i++ ){
// cout << fi[i].rmul << " " << fi[i].amul << " " << fi[i].c << endl;
//}
}
/*
s(i) = a のとき
r, s(i) .. s(i+n-1) をつなげた数をMで割った余りを返す
*/
ll f( ll r, ll a, ll n, ll keta, ll k ){
calc_fi( r, a, keta, k );
for ( int i = 0; n; i++ ){
ll p = 1LL << i;
if ( n & p ){
r = (fi[i].rmul*r + fi[i].amul*a + fi[i].c)%M;
a = (a + BM*(p%M))%M;
n -= p;
}
}
return r;
}
int main(){
cin >> L >> A >> B >> M;
AM = A % M;
BM = B % M;
ll result = 0;
for ( ll keta = 1, k = 10; keta <= 18; keta++, k *= 10 ){ // k = 10^keta
// k/10 <= s < k となる範囲の s を処理する
if ( k/10 <= A && A < k ){
// k <= A+nB となるnは?
// (k-A)/B <= n
ll n = (k-A+B-1)/B;
if ( n > L )
n = L;
//cout << "\n\nrange: " << A << " - " << (A + B * (n-1)) << " : n=" << n << endl;
//ll rtest = result;
//for ( int j = 0; j < n; j++ ){
// rtest = ((rtest*(k%M))%M + (AM + BM*j%M)%M)%M;
//}
//cout << "rtest: " << rtest << endl;
result = f( result, AM, n, keta, k );
//cout << "result: " << result << endl;
A += B * n;
AM = A % M;
L -= n;
if ( L == 0 )
break;
}
}
cout << result << endl;
return 0;
}
|
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#define REP(i,n) for(int i=0;i<n;i++)
#define REPP(i,n) for(int i=1;i<=n;i++)
#define ALL(obj) (obj).begin(), (obj).end()
const double PI = acos(-1);
const double EPS = 1e-15;
long long INF=(long long)1E17;
#define i_7 (long long)(1E9+7)
long mod(long a){
long long c=a%i_7;
if(c>=0)return c;
return c+i_7;
}
using namespace std;
long long po(long long a, long long b, long long m){
if(b==0){
return 1;
}
long long z = po(a,b/2,m);
z = (z*z)%m;
if(b%2!=0){
z = (a*z)%m;
}
return z;
}
bool prime_(int n){
if(n==1){
return false;
}else if(n==2){
return true;
}else{
for(int i=2;i<=sqrt(n);i++){
if(n%i==0){
return false;
}
}
return true;
}
}
long long gcd_(long long a, long long b){
if(a<b){
swap(a,b);
}
if(a%b==0){
return b;
}else{
return gcd_(b,a%b);
}
}
long long lcm_(long long x, long long y){
return (x/gcd_(x,y))*y;
}
int main(){
long long l,a,b,m;
cin>>l>>a>>b>>m;
long long c;
long long power = 1;
long long ans[3];
ans[0] = 0;
ans[1] = a%m;
ans[2] = 1LL;
for(long long d = 1; d<=18; d++){
long long left, right;
left = ((power - a) + b - 1)/b;
if(left>=l){
power *= 10LL;
continue;
}
left = max(left, 0LL);
right = ((10LL*power - a) + b - 1)/b;
if(right<=0){
power *= 10LL;
continue;
}
right = min(right, l);
if(right<left){
power *= 10LL;
continue;
}
c = right - left;
//cout<<c<<endl;
power *= 10LL;
long long mat[3][3] = {};
mat[0][0] = po(10LL, d, m);
mat[1][0] = mat[1][1] = mat[2][2] = 1LL;
mat[2][1] = b%m;
while(c>0){
if(c & 1){
long long temp[3] = {};
REP(i,3){
REP(j,3){
temp[i] += (ans[j]*mat[j][i])%m;
temp[i] %= m;
}
}
REP(i,3){
ans[i] = temp[i];
}
}
c /= 2;
long long tempMat[3][3] = {};
REP(i,3){
REP(j,3){
REP(k,3){
tempMat[i][j] += (mat[i][k]*mat[k][j])%m;
tempMat[i][j] %= m;
}
}
}
REP(i,3){
REP(j,3){
mat[i][j] = tempMat[i][j];
}
}
}
}
cout<<ans[0]<<endl;
return 0;
}
|
#include <bits/stdc++.h>
#define fst(t) std::get<0>(t)
#define snd(t) std::get<1>(t)
#define thd(t) std::get<2>(t)
#define unless(p) if(!(p))
#define until(p) while(!(p))
using ll = std::int64_t;
using P = std::tuple<int,int>;
template <typename T>
std::tuple<T, T, T> extgcd(T a, T b){
T s1 = 1, t1 = 0, s2 = 0, t2 = 1;
while(b != 0){
std::tie(s1, t1, s2, t2) = std::make_tuple(s2, t2, s1 - (a / b) * s2, t1 - (a / b) * t2);
std::tie(a, b) = std::make_tuple(b, a % b);
}
return std::make_tuple(s1, t1, a);
}
template <typename T>
T mod_expt(T a, std::int64_t n, T mod){
T power {1};
while(n > 0){
if(n & 1){power = power * a % mod;}
a = a * a % mod;
n >>= 1;
}
return power;
}
// 注意: a と mod が互いに素である必要がある
template <typename T>
T mod_inverse(T a, T mod){
T b;
std::tie(b, std::ignore, std::ignore) = extgcd(a, mod);
if(b < 0){b += mod;}
return b;
}
ll L, A, B, M;
ll f(ll x, ll n){
if(n == 0){
return 0;
}
if(n % 2 == 0){
return f(x, n / 2) * (1ll + mod_expt(x, n / 2, M)) % M;
}
return (1ll + f(x, n - 1) * x % M) % M;
}
ll g(ll x, ll n){
if(n == 0){
return 0;
}
if(n % 2 == 0){
return (g(x, n / 2) * (1ll + mod_expt(x, n / 2, M)) % M + (n / 2) % M * f(x, n / 2) % M) % M;
}
return ((n - 1) % M + g(x, n - 1) * x % M) % M;
}
int main(){
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
std::cin >> L >> A >> B >> M;
ll l = 0, ten = 1;
ll res = 0;
for(int i=1;i<=18;++i){
ll s = A + B * l;
unless(ten <= s && s < ten * 10){
ten *= 10;
continue;
}
ll r = std::min((ten * 10 - A + B - 1) / B, L), n = r - l;
ll a = res * mod_expt(ten * 10 % M, n, M) % M,
b = A % M * f(ten * 10 % M, n) % M,
c = B % M * (g(ten * 10 % M, r) + M - g(ten * 10 % M, l) * mod_expt(ten * 10 % M, n, M) % M) % M;
res = (a + b + c) % M;
l = r;
ten *= 10;
}
std::cout << res << std::endl;
}
|
#include <bits/stdc++.h>
#define IO_OP std::ios::sync_with_stdio(0); std::cin.tie(0);
#define F first
#define S second
#define PB push_back
#define MP make_pair
#define EB emplace_back
#define int ll
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef vector<int> vi;
const int INF = 1e9 + 7;
int m;
class M{
public:
ll a[3][3];
M() {
memset(a, 0, sizeof a);
}
M operator*(M b) {
M c;
for(int i=0;i<3;i++) {
for(int j=0;j<3;j++) {
for(int k=0;k<3;k++) {
c.a[i][j] += a[i][k] * b.a[k][j] % m;
c.a[i][j] %= m;
}
}
}
return c;
}
};
M pw(M A, int b) {
if(b == 0) {
M id;
for(int i=0;i<3;i++)
id.a[i][i] = 1;
return id;
}
M T = pw(A, b/2);
if(b & 1) {
return T * T * A;
} else {
return T * T;
}
}
int32_t main()
{
IO_OP;
int L, a, b, p = 1;
cin >> L >> a >> b >> m;
M v;
v.a[0][0] = 0, v.a[1][0] = a % m, v.a[2][0] = b % m;
for(int w=1;w<=18;w++,p *= 10) {
int l = max((p-a+b-1)/b + 1, 1LL);
int r = (p*10-a+b-1)/b;
// cout << l << " " << r << endl;
// cout << v.a[0][0] << endl;
if(l > L) break;
if(r < l)
continue;
r = min(r, L);
int k = r - l + 1;
M A;
A.a[0][0] = p * 10 % m;
A.a[0][1] = 1;
A.a[1][1] = 1;
A.a[1][2] = 1;
A.a[2][2] = 1;
A = pw(A, k);
v = A * v;
}
cout << v.a[0][0] << endl;
}
|
#include<bits/stdc++.h>
#include <array>
using namespace std;
using ULL = unsigned long long;
using UL = unsigned;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)
ULL MOD;
struct Matrix {
ULL M[3][3] = { {1,0,0}, {0,1,0}, {0,0,1} };
Matrix operator*(const Matrix &r) const {
Matrix t;
rep(x, 3) rep(y, 3) {
t.M[x][y] = 0;
rep(i, 3) {
t.M[x][y] += M[i][y] * r.M[x][i];
t.M[x][y] %= MOD;
}
}
return t;
}
};
Matrix Pow(const Matrix &a, ULL p) {
if (p == 0) return Matrix();
if (p == 1) return a;
Matrix tmp = Pow(a, p / 2);
tmp = tmp * tmp;
if (p % 2 == 1) tmp = tmp * a;
return tmp;
}
ULL Pow(const ULL &a, ULL p) {
if (p == 1) return a;
ULL tmp = Pow(a, p / 2);
tmp = tmp * tmp % MOD;
if (p % 2 == 1) tmp = tmp * a % MOD;
return tmp;
}
struct Problem {
ULL ans = 0;
void Solve2(ULL Len, ULL A, ULL B, ULL P) {
Matrix Mx;
Mx.M[0][0] = P % MOD; Mx.M[1][0] = 0; Mx.M[2][0] = 0;
Mx.M[0][1] = 1; Mx.M[1][1] = 1; Mx.M[2][1] = 0;
Mx.M[0][2] = 0; Mx.M[1][2] = B % MOD; Mx.M[2][2] = 1;
Mx = Pow(Mx, Len);
ans = ans * Mx.M[0][0] + A % MOD * Mx.M[0][1] + Mx.M[0][2];
ans %= MOD;
}
void Solve() {
ULL Len, A, B; cin >> Len >> A >> B >> MOD;
ULL R = A + B * Len;
rep(i, 18) {
ULL P = 1; rep(j, i) P *= 10;
ULL Lb = P, Rb = P * 10;
if (R <= Lb) continue;
if (A >= Rb) continue;
Lb = max(Lb, A);
Rb = min(Rb, R);
Lb = (Lb + B - 1 - A) / B * B + A;
Rb = (Rb + B - 1 - A) / B * B + A;
Solve2((Rb - Lb) / B, Lb, B, P * 10);
}
cout << ans << endl;
}
Problem();
};
int main() {
unique_ptr<Problem> p(new Problem());
p->Solve();
return 0;
}
Problem::Problem() {
cout << fixed << setprecision(10);
} |
#include <iostream>
using namespace std;
long long modPow(long long a, long long p, long long mod){
if(p == 0) return 1;
auto res = modPow(a, p/2, mod);
res = (res * res) % mod;
if(p%2) res = (res * a) % mod;
return res;
}
long long repMod(long long a, long long p, long long d, long long mod){
if(p == 0) return 0;
auto res = repMod(a, p/2, d, mod);
res *= modPow(10, d*(p/2), mod) + 1;
res %= mod;
if(p%2){
res = modPow(10, d, mod) * res + a;
res %= mod;
}
return res;
}
long long calc(long long a, long long b, long long d, long long L, long long mod){
if(L == 0) return 0;
auto res = calc(a, b, d, L/2, mod);
res *= modPow(10, d*(L/2), mod) + 1;
res %= mod;
res += repMod(L/2*b, L/2, d, mod);
res %= mod;
if(L%2){
res = modPow(10, d, mod) * res + a + (L-1)*b;
res %= mod;
}
return res;
}
int main(){
long long L, A, B, M;
while(cin >> L >> A >> B >> M){
int d = 0; long long n10 = 1;
while(n10 <= A){
d++;
n10 *= 10;
}
long long res = 0;
while(L > 0){
long long l = min(L, (n10 - A + B - 1) / B);
res *= modPow(modPow(10, l, M), d, M);
res %= M;
res += calc(A, B, d, l, M);
res %= M;
A += B * l;
L -= l;
n10 *= 10;
d++;
}
cout << res << endl;
}
} |
#include <bits/stdc++.h>
#define rep(i, a, b) for(ll i = ll(a); i < ll(b); i++)
#define rer(i, a, b) for(ll i = ll(a) - 1; i >= ll(b); i--)
#define sz(v) (int)(v).size()
#define pb push_back
#define sc second
#define fr first
#define sor(v) sort(v.begin(),v.end())
#define rev(s) reverse(s.begin(),s.end())
#define lb(vec,a) lower_bound(vec.begin(),vec.end(),a)
#define ub(vec,a) upper_bound(vec.begin(),vec.end(),a)
#define uniq(vec) vec.erase(unique(vec.begin(),vec.end()),vec.end())
using namespace std;
typedef long long int ll;
typedef __int128_t lll;
typedef pair <int, int> P;
typedef vector<lll> vec;
typedef vector<vec> mat;
ll MOD;
ll L,A,B;
mat mul(mat A, mat B){
mat C(A.size(), vec(B[0].size()));
rep(i,0,A.size()){
rep(k,0,B.size()){
rep(j,0,B[0].size()){
C[i][j]+=A[i][k]*B[k][j]%MOD;
C[i][j]%=MOD;
}
}
}
return C;
}
mat pow(mat A, ll n){
mat B(A.size(), vec(A.size()));
rep(i,0,A.size()){
B[i][i]=1;
}
while(n>0){
if(n&1) B=mul(B,A);
A=mul(A,A);
n>>=1;
}
return B;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin>>L>>A>>B>>MOD;
ll last=A+B*(L-1);
ll ans=0;
bool X=true;
while(X){
ll ret=1, rett=1;
rep(i,0,19){
if(A<ret){
break;
}
else{
ret*=10;
rett=ret%MOD;
}
}
ll u=ret;
ll n=(u-A-1)/B;
if(last<u){
n=(last-A)/B;
X=false;
}
mat a(3,vec(3,0));
mat b(3, vec(1,0));
a[0][0]=rett; a[0][1]=1; a[0][2]=0;
a[1][0]=0; a[1][1]=1; a[1][2]=B%MOD;
a[2][0]=0; a[2][1]=0; a[2][2]=1;
b[0][0]=ans; b[1][0]=A; b[2][0]=1;
a=mul(pow(a,n+1), b);
ans=a[0][0];
A=A+B*(n+1);
}
cout <<ans<<"\n";
} |
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
#define p_ary(ary,a,b,i) do { cout << "["; for (int (i) = (a);(i) < (b);++(i)) cout << ary[(i)] << ((b)-1 == (i) ? "" : ", "); cout << "]\n"; } while(0)
#define p_map(map,it) do {cout << "{";for (auto (it) = map.begin();;++(it)) {if ((it) == map.end()) {cout << "}\n";break;}else cout << "" << (it)->first << "=>" << (it)->second << ", ";}}while(0)
vector<vector<ll>> prod(vector<vector<ll>>& a, vector<vector<ll>>& b, ll mod) {
vector<vector<ll>> ret(a.size(),vector<ll>(b[0].size(),0));
for (int i = 0;i < a.size();++i) for (int j = 0;j < b[0].size();++j) for (int k = 0;k < a[0].size();++k) {
ret[i][j] += a[i][k]*b[k][j];
ret[i][j] %= mod;
}
return ret;
}
int main() {
ll l,a,b,m;
cin >> l >> a >> b >> m;
// m = 1e18;
l--;
vector<ll> c(20,0);
for (int i = 0;i < 19;++i) {
ll d = 1;
for (int j = 0;j < i;++j) d *= 10;
c[i] = max(0LL,(d-a-1)/b);
}
c[19] = 2e18;
vector<vector<ll>> x(3,vector<ll>(1,0)),y(3,vector<ll>(3,0));
x[0][0] = x[1][0] = a%m;
x[2][0] = b%m;
for (int i = 1;i < 20;++i) {
ll d = 1;
for (int j = 0;j < i;++j) (d *= 10) %= m;
y[0][1] = y[0][2] = y[1][1] = y[1][2] = y[2][2] = 1;
y[0][0] = d;
// for (int j = 0;j < 3;++j) p_ary(y[j],0,3,k);
// for (int j = 0;j < 3;++j) p_ary(x[j],0,1,k);
ll z = min(l,c[i])-c[i-1];
// cout << z << endl;
while (z > 0) {
if (z&1) x = prod(y,x,m);
y = prod(y,y,m);
z >>= 1;
}
// for (int j = 0;j < 3;++j) p_ary(y[j],0,3,k);
// for (int j = 0;j < 3;++j) p_ary(x[j],0,1,k);
if (l <= c[i]) break;
}
cout << x[0][0] << endl;
// for (int i = 0;i < 20;++i) cout << a+b*c[i] << " " << a+b*(c[i]+1) << endl;
// p_ary(c,0,20,i);
} |
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
typedef long long ll;
int main(){
int n,a,b; cin>>n>>a>>b;
int cnta=0, cntb=0, cntc=0;
rep(i,n){
int p; cin>>p;
if(p<=a) cnta++;
else if(p>a&&p<=b) cntb++;
else cntc++;
}
cout<<min(cnta,min(cntb,cntc))<<endl;
} |
#include <bits/stdc++.h>
using namespace std;
int main() {
int n,a,b;cin>>n>>a>>b;
vector<int> c(n);
int p=0,q=0,r=0;
for(int i=0;i<n;++i) {
cin>>c[i];
if(c[i]<=a) ++p;
else if(c[i]<=b) ++q;
else ++r;
}
int ans = min(p,min(q,r));
cout<<ans<<endl;
} |
#include <bits/stdc++.h>
#define int long long
using namespace std;
signed main(){
int N,A,B;
cin>>N>>A>>B;
int a,b,c;
a=b=c=0;int k;
for(int i=0;i<N;i++){
cin>>k;
if(k<=A)a++;
else if(k>B)b++;
else c++;
}
cout<<min(a,min(b,c))<<endl;
}
|
#include<bits/stdc++.h>
using namespace std;
int x,n,n1,n2,n3,a,b;
int main() {
cin>>n>>a>>b;
for(int i=1;i<=n;++i) {
cin>>x;
if(x<=a) n1++;
else if(x>a && x<=b) n2++;
else n3++;
}
cout<<min(n1,min(n2,n3));
} |
#include<bits/stdc++.h>
using namespace std;
int main()
{
int n,A,B;
cin>>n>>A>>B;
int t1=0,t2=0,t3=0;
for (int i=1;i<=n;i++) {
int x; scanf("%d",&x);
if (x<=A) t1++;
if (x>A && x<=B) t2++;
if (x>B) t3++;
}
cout<<min(t1,min(t2,t3));
}
|
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int main(){
int n,a,b;
cin>>n>>a>>b;
vector<int> v(3);
for(int i=0;i<n;i++){
int p;
cin>>p;
v[(p<=a)+(p<=b)]++;
}
cout<<*min_element(v.begin(),v.end())<<"\n";
}
|
#include <iostream>
#include <algorithm>
#include <string>
using namespace std;
typedef long long int ll;
int main(){
ll n,a,b;
cin >>n;
cin >>a>>b;
ll p[n],aa=0,ab=0,bb=0;
for(ll i=0;i<n;i++) {
cin >>p[i];
if(p[i]<=a) aa++;
else if(p[i]<=b) ab++;
else bb++;
}
cout << min(bb,min(aa,ab))<<endl;
}
|
#include<bits/stdc++.h>
using namespace std;
int main(){
int n,a,b,p=0,q=0,r=0;
cin>>n>>a>>b;
for(int i=0;i<n;++i){
int k;
cin>>k;
if(k<=a)p++;
else if(k<=b)q++;
else r++;
}
cout<<min({p,q,r})<<"\n";
return 0;
} |
#include <stdio.h>
int main(void){
int n,a,b,p,i,x[3]={},min=100;
scanf("%d%d%d",&n,&a,&b);
for (i=0;i<n;i++){
scanf("%d",&p);
if (p<=a) x[0]++;
else if (p<=b) x[1]++;
else x[2]++;
}
for (i=0;i<3;i++){
if (min>x[i]) min=x[i];
}
printf("%d\n",min);
return 0;
}
|
#include <iostream>
#include <vector>
using namespace std;
int x,y,z;
int main() {
int n,a,b,vec;
cin>>n>>a>>b;
for(int i=0;i<n;i++){
cin>>vec;
if(vec<=a){
x++;
}
else if(vec<=b){
y++;
}
else{
z++;
}
}
cout<<min(min(x,y),z)<<endl;
} |
#include<bits/stdc++.h>
using namespace std;
int a[105],b[3];
int main()
{
int n,x,y,i;
cin>>n>>x>>y;
for(i=1;i<=n;i++)
{
cin>>a[i];
if(a[i]<=x)
b[0]++;
if(a[i]>=x+1&&a[i]<=y)
b[1]++;
if(a[i]>=y+1)
b[2]++;
}
sort(b,b+3);
cout<<b[0];
return 0;
} |
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