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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#341790 | #7954. Special Numbers | ucup-team2981# | AC ✓ | 19ms | 6484kb | C++20 | 9.9kb | 2024-02-29 21:23:06 | 2024-02-29 21:23:12 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
template<class data_t, data_t _mod>
struct modular_fixed_base{
#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)
static_assert(IS_UNSIGNED(data_t));
static_assert(_mod >= 1);
static constexpr bool VARIATE_MOD_FLAG = false;
static constexpr data_t mod(){
return _mod;
}
template<class T>
static vector<modular_fixed_base> precalc_power(T base, int SZ){
vector<modular_fixed_base> res(SZ + 1, 1);
for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
return res;
}
static vector<modular_fixed_base> _INV;
static void precalc_inverse(int SZ){
if(_INV.empty()) _INV.assign(2, 1);
for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
}
// _mod must be a prime
static modular_fixed_base _primitive_root;
static modular_fixed_base primitive_root(){
if(_primitive_root) return _primitive_root;
if(_mod == 2) return _primitive_root = 1;
if(_mod == 998244353) return _primitive_root = 3;
data_t divs[20] = {};
divs[0] = 2;
int cnt = 1;
data_t x = (_mod - 1) / 2;
while(x % 2 == 0) x /= 2;
for(auto i = 3; 1LL * i * i <= x; i += 2){
if(x % i == 0){
divs[cnt ++] = i;
while(x % i == 0) x /= i;
}
}
if(x > 1) divs[cnt ++] = x;
for(auto g = 2; ; ++ g){
bool ok = true;
for(auto i = 0; i < cnt; ++ i){
if((modular_fixed_base(g).power((_mod - 1) / divs[i])) == 1){
ok = false;
break;
}
}
if(ok) return _primitive_root = g;
}
}
constexpr modular_fixed_base(){ }
modular_fixed_base(const double &x){ data = _normalize(llround(x)); }
modular_fixed_base(const long double &x){ data = _normalize(llround(x)); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){
int sign = x >= 0 ? 1 : -1;
data_t v = _mod <= sign * x ? sign * x % _mod : sign * x;
if(sign == -1 && v) v = _mod - v;
return v;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data; }
modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
modular_fixed_base &operator++(){ return *this += 1; }
modular_fixed_base &operator--(){ return *this += _mod - 1; }
modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
modular_fixed_base &operator*=(const modular_fixed_base &rhs){
if constexpr(is_same_v<data_t, unsigned int>) data = (unsigned long long)data * rhs.data % _mod;
else if constexpr(is_same_v<data_t, unsigned long long>){
long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data);
data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);
}
else data = _normalize(data * rhs.data);
return *this;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base &inplace_power(T e){
if(e == 0) return *this = 1;
if(data == 0) return *this = {};
if(data == 1) return *this;
if(data == mod() - 1) return e % 2 ? *this : *this = -*this;
if(e < 0) *this = 1 / *this, e = -e;
modular_fixed_base res = 1;
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base power(T e) const{
return modular_fixed_base(*this).inplace_power(e);
}
modular_fixed_base &operator/=(const modular_fixed_base &otr){
make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;
if(a < _INV.size()) return *this *= _INV[a];
while(a){
make_signed_t<data_t> t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return *this *= u;
}
#define ARITHMETIC_OP(op, apply_op)\
modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }
ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; }
COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
friend istream &operator>>(istream &in, modular_fixed_base &number){
long long x;
in >> x;
number.data = modular_fixed_base::_normalize(x);
return in;
}
//#define _SHOW_FRACTION
friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
out << number.data;
#if defined(LOCAL) && defined(_SHOW_FRACTION)
cerr << "(";
for(auto d = 1; ; ++ d){
if((number * d).data <= 1000000){
cerr << (number * d).data;
if(d != 1) cerr << "/" << d;
break;
}
else if((-number * d).data <= 1000000){
cerr << "-" << (-number * d).data;
if(d != 1) cerr << "/" << d;
break;
}
}
cerr << ")";
#endif
return out;
}
data_t data = 0;
#undef _SHOW_FRACTION
#undef IS_INTEGRAL
#undef IS_SIGNED
};
template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;
template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;
// const unsigned int mod = (119 << 23) + 1; // 998244353
const unsigned int mod = 1e9 + 7; // 1000000007
// const unsigned int mod = 1e9 + 9; // 1000000009
// const unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
if (fopen("KEK.inp", "r")){
freopen("KEK.inp", "r", stdin);
freopen("KEK.out", "w", stdout);
}
ll k;
string l, r;
cin >> k >> l >> r;
int m = -1;
vector <ll> vdivisor;
vector <array <int, 10>> transition;
auto prepare_divisor = [&](){
ll tk = k;
vector <pair <int, int>> vpf;
for (auto p: vector <int>{{2, 3, 5, 7}}){
int q = 0;
while (tk % p == 0){
tk /= p;
q++;
}
vpf.emplace_back(p, q);
}
if (tk != 1){
m = 2;
transition.resize(2);
transition[0].fill(0);
transition[1].fill(1);
transition[0][0] = 1;
return;
}
auto backtrack = [&](auto self, int i, ll cur = 1){
if (i == ssize(vpf)){
vdivisor.emplace_back(cur);
return;
}
self(self, i + 1, cur);
for (int j = 0; j < vpf[i].second; j++){
cur *= vpf[i].first;
self(self, i + 1, cur);
}
};
backtrack(backtrack, 0);
m = ssize(vdivisor);
sort(vdivisor.begin(), vdivisor.end());
transition.resize(m);
for (int i = 0; i < m; i++){
ll val = vdivisor[i];
vector <pair <int, int>> vpf_val;
{
ll tval = val;
for (auto p: vector <int>{{2, 3, 5, 7}}){
int q = 0;
while (tval % p == 0){
tval /= p;
q++;
}
vpf_val.emplace_back(p, q);
}
}
transition[i][0] = m - 1;
for (int d = 1; d <= 9; d++){
ll tval = val;
int td = d;
for (int idx = 0; idx < ssize(vpf); idx++){
int p = vpf[idx].first, q = vpf[idx].second - vpf_val[idx].second;
while (td % p == 0 and q > 0){
tval *= p;
td /= p;
q--;
}
}
int j = lower_bound(begin(vdivisor), end(vdivisor), tval) - begin(vdivisor);
transition[i][d] = j;
}
}
};
prepare_divisor();
int n = -1;
{
reverse(begin(l), end(l));
reverse(begin(r), end(r));
while (ssize(l) < ssize(r)){
l += '0';
}
while (ssize(r) < ssize(l)){
r += '0';
}
n = ssize(l);
}
vector <vector <vector <vector <vector <modular>>>>> dp(n + 1, vector <vector <vector <vector <modular>>>>(2, vector <vector <vector <modular>>>(2, vector <vector <modular>>(2, vector <modular>(m, modular(0))))));
for (int touch_l = 0; touch_l <= 1; touch_l++){
for (int touch_r = 0; touch_r <= 1; touch_r++){
dp[0][1][touch_l][touch_r][m - 1] = modular(1);
}
}
for (int d = 1; d <= n; d++){
for (int started = 0; started <= 1; started++){
for (int touch_l = 0; touch_l <= 1; touch_l++){
for (int touch_r = 0; touch_r <= 1; touch_r++){
int ldig = touch_l ? int(l[d - 1] - '0') : 0;
int rdig = touch_r ? int(r[d - 1] - '0') : 9;
for (int i = 0; i < m; i++){
for (int dig = ldig; dig <= rdig; dig++){
dp[d][started][touch_l][touch_r][i] += dp[d - 1][started | (dig != 0)][touch_l & (dig == ldig)][touch_r & (dig == rdig)][(started | (dig != 0)) ? transition[i][dig] : 0];
}
}
}
}
}
}
modular ans = dp[n][0][1][1][0];
cout << ans << "\n";
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3636kb
input:
5 1 20
output:
4
result:
ok single line: '4'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3660kb
input:
5 50 100
output:
19
result:
ok single line: '19'
Test #3:
score: 0
Accepted
time: 0ms
memory: 3632kb
input:
15 11 19
output:
0
result:
ok single line: '0'
Test #4:
score: 0
Accepted
time: 1ms
memory: 3692kb
input:
1 100 100000
output:
99901
result:
ok single line: '99901'
Test #5:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
1 1 1
output:
1
result:
ok single line: '1'
Test #6:
score: 0
Accepted
time: 0ms
memory: 3684kb
input:
10 800 43021
output:
23570
result:
ok single line: '23570'
Test #7:
score: 0
Accepted
time: 1ms
memory: 3684kb
input:
1125899906842624 1 100000000000000000000
output:
555058180
result:
ok single line: '555058180'
Test #8:
score: 0
Accepted
time: 1ms
memory: 3804kb
input:
187500000 5941554024261918062 17356601866920567143
output:
679191360
result:
ok single line: '679191360'
Test #9:
score: 0
Accepted
time: 0ms
memory: 3944kb
input:
1555848 157165614890794026 49792374427566422833
output:
588832126
result:
ok single line: '588832126'
Test #10:
score: 0
Accepted
time: 11ms
memory: 5440kb
input:
53814924637488000 8378901287491856069 46225409092942057365
output:
964965504
result:
ok single line: '964965504'
Test #11:
score: 0
Accepted
time: 19ms
memory: 6484kb
input:
11814720750000000 8152927138245188051 35351923956338524619
output:
183963359
result:
ok single line: '183963359'
Test #12:
score: 0
Accepted
time: 6ms
memory: 4192kb
input:
6453888000000 4334845344448208535 35982793193772682339
output:
570114022
result:
ok single line: '570114022'
Test #13:
score: 0
Accepted
time: 9ms
memory: 4776kb
input:
90071357282285400 7893548167754114409 27099084703937108974
output:
869822186
result:
ok single line: '869822186'
Test #14:
score: 0
Accepted
time: 11ms
memory: 4692kb
input:
45571065750000 177160749596350425 98884377930460959454
output:
607698665
result:
ok single line: '607698665'
Test #15:
score: 0
Accepted
time: 5ms
memory: 3932kb
input:
1128443962982400 6338876482181492537 40931938533793596007
output:
881168270
result:
ok single line: '881168270'
Test #16:
score: 0
Accepted
time: 0ms
memory: 3680kb
input:
1 1 1
output:
1
result:
ok single line: '1'
Test #17:
score: 0
Accepted
time: 5ms
memory: 3944kb
input:
1412793457031250 2410155470167050095 99063185266833009818
output:
399813226
result:
ok single line: '399813226'
Test #18:
score: 0
Accepted
time: 7ms
memory: 4760kb
input:
67722117120000 8909573534349989418 73129289758235281558
output:
898227227
result:
ok single line: '898227227'
Test #19:
score: 0
Accepted
time: 4ms
memory: 4156kb
input:
472055808000 6809917603531307093 27494416416722163137
output:
379198478
result:
ok single line: '379198478'
Test #20:
score: 0
Accepted
time: 4ms
memory: 3796kb
input:
19353600000 8687492345912514346 24058039408337150852
output:
250715555
result:
ok single line: '250715555'
Test #21:
score: 0
Accepted
time: 3ms
memory: 4148kb
input:
47855420020225440 6150828649270625443 84863934988301168136
output:
665186711
result:
ok single line: '665186711'
Test #22:
score: 0
Accepted
time: 2ms
memory: 3992kb
input:
1382400000 9545797804645162278 70441077437727026904
output:
278230087
result:
ok single line: '278230087'
Test #23:
score: 0
Accepted
time: 1ms
memory: 3752kb
input:
816293376 2952089614708276156 10939708785225040670
output:
120954190
result:
ok single line: '120954190'
Test #24:
score: 0
Accepted
time: 1ms
memory: 3800kb
input:
4185097875 1348426133484952253 56617823359794500344
output:
773995224
result:
ok single line: '773995224'
Test #25:
score: 0
Accepted
time: 0ms
memory: 4404kb
input:
5828945117184 7777082394971366991 63470232991138132969
output:
678496908
result:
ok single line: '678496908'
Test #26:
score: 0
Accepted
time: 3ms
memory: 4324kb
input:
16184770560 3869053219872876321 94590086601168840932
output:
168181821
result:
ok single line: '168181821'
Test #27:
score: 0
Accepted
time: 0ms
memory: 3692kb
input:
2 1 12
output:
6
result:
ok single line: '6'
Test #28:
score: 0
Accepted
time: 1ms
memory: 3748kb
input:
30146484375 290228705524339176 51853415145287716863
output:
229436627
result:
ok single line: '229436627'
Test #29:
score: 0
Accepted
time: 5ms
memory: 4248kb
input:
2072513819443200 3726664558969607832 42501102605103061370
output:
947952932
result:
ok single line: '947952932'
Test #30:
score: 0
Accepted
time: 16ms
memory: 5528kb
input:
9920232000000000 4602219263214498291 80783137037024823899
output:
846877519
result:
ok single line: '846877519'
Test #31:
score: 0
Accepted
time: 7ms
memory: 4412kb
input:
97200000000000000 9310820760839688870 35322929083473756214
output:
936587432
result:
ok single line: '936587432'
Test #32:
score: 0
Accepted
time: 2ms
memory: 3920kb
input:
45209390625 5752361069878044328 64635325028527078951
output:
578047592
result:
ok single line: '578047592'
Test #33:
score: 0
Accepted
time: 15ms
memory: 5468kb
input:
54442233216000 2452030574225118723 90982734056131320662
output:
417646585
result:
ok single line: '417646585'
Test #34:
score: 0
Accepted
time: 4ms
memory: 4220kb
input:
1530550080000 7431421026778839808 84825282227911272129
output:
600103842
result:
ok single line: '600103842'
Test #35:
score: 0
Accepted
time: 7ms
memory: 4456kb
input:
13765147361280 4924477486471254843 10002324705150566233
output:
951883713
result:
ok single line: '951883713'
Test #36:
score: 0
Accepted
time: 4ms
memory: 4504kb
input:
59825698242187500 6303744363677706767 91410210495502213963
output:
774734375
result:
ok single line: '774734375'
Test #37:
score: 0
Accepted
time: 10ms
memory: 4764kb
input:
110658879959040 2133591391458550040 48494371567095341228
output:
103505650
result:
ok single line: '103505650'
Test #38:
score: 0
Accepted
time: 0ms
memory: 3628kb
input:
1 3 100
output:
98
result:
ok single line: '98'
Test #39:
score: 0
Accepted
time: 8ms
memory: 4648kb
input:
3160365465600 8968721517098518892 78444481529635953131
output:
364620926
result:
ok single line: '364620926'
Test #40:
score: 0
Accepted
time: 0ms
memory: 3936kb
input:
54838448056132899 4242999884713464056 92948071680698209741
output:
922087167
result:
ok single line: '922087167'
Test #41:
score: 0
Accepted
time: 0ms
memory: 3652kb
input:
78183771565555182 7823307199080715671 93466469990450000599
output:
635073629
result:
ok single line: '635073629'
Test #42:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
56555532446322947 2952925229100796893 35926880503684324113
output:
663547216
result:
ok single line: '663547216'
Test #43:
score: 0
Accepted
time: 0ms
memory: 3700kb
input:
15701121272683095 8633703383009071570 55273589042372583668
output:
253996413
result:
ok single line: '253996413'
Test #44:
score: 0
Accepted
time: 0ms
memory: 3936kb
input:
11914467542453704 2857068399817941722 83230805830740136213
output:
956698341
result:
ok single line: '956698341'
Test #45:
score: 0
Accepted
time: 0ms
memory: 3716kb
input:
28181999963152819 7948365158338416594 87742700746768593189
output:
720016372
result:
ok single line: '720016372'
Test #46:
score: 0
Accepted
time: 0ms
memory: 3640kb
input:
85409868208332321 3921672860136397259 55474188860042435613
output:
622329181
result:
ok single line: '622329181'
Test #47:
score: 0
Accepted
time: 0ms
memory: 3676kb
input:
14748052718175068 9293071633738211123 85443373435217434149
output:
38392129
result:
ok single line: '38392129'
Test #48:
score: 0
Accepted
time: 0ms
memory: 3712kb
input:
41002058985303228 6141335647135876923 78910335860595680506
output:
665823537
result:
ok single line: '665823537'
Test #49:
score: 0
Accepted
time: 0ms
memory: 3856kb
input:
4 3 123
output:
62
result:
ok single line: '62'
Test #50:
score: 0
Accepted
time: 0ms
memory: 3952kb
input:
100000000000000000 3 100000000000000000000
output:
302574822
result:
ok single line: '302574822'
Test #51:
score: 0
Accepted
time: 0ms
memory: 3664kb
input:
6 7 12034
output:
9505
result:
ok single line: '9505'
Test #52:
score: 0
Accepted
time: 0ms
memory: 3692kb
input:
7 8 43021
output:
25028
result:
ok single line: '25028'
Test #53:
score: 0
Accepted
time: 0ms
memory: 3688kb
input:
8 8 43021
output:
32619
result:
ok single line: '32619'
Test #54:
score: 0
Accepted
time: 0ms
memory: 3580kb
input:
9 800 43021
output:
30930
result:
ok single line: '30930'