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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#826757 | #4283. Power of XOR | Zi_Gao | RE | 1ms | 5844kb | C++20 | 4.5kb | 2024-12-22 15:55:18 | 2024-12-22 15:55:18 |
Judging History
answer
#include<bits/stdc++.h>
// #define ONLINE_JUDGE
#define INPUT_DATA_TYPE long long
#define OUTPUT_DATA_TYPE int
inline __attribute((always_inline)) INPUT_DATA_TYPE read(){register INPUT_DATA_TYPE x=0;register char f=0,c=getchar();while(c<'0'||'9'<c)f=(c=='-'),c=getchar();while('0'<=c&&c<='9')x=(x<<3)+(x<<1)+(c&15),c=getchar();return f?-x:x;}void print(OUTPUT_DATA_TYPE x){if(x<0)x=-x,putchar('-');if(x>9)print(x/10);putchar(x%10^48);return;}
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
using mint=LazyMontgomeryModInt<1000'000'007>;
const int W=44;
mint pw2=1;
struct LBASE{
long long p[W];
void insert(long long x){
register int i;
for(i=W-1;~i;--i) if((x>>i)&1){
if(p[i]) x^=p[i];
else return p[i]=x,void();
}
pw2*=2;
}
void solve(){
register int i,j;
for(i=0;i<W;++i) if(p[i]) for(j=i+1;j<W;++j) if((p[j]>>i)&1) p[j]^=p[i];
}
}lb;
const int Bs=17;
const int Bb=W-Bs;
int pos[W];
long long val[1<<Bs],num[Bb];
mint pw[W],dp[Bb][1<<Bs];
int main(){
#ifndef ONLINE_JUDGE
freopen("name.in", "r", stdin);
freopen("name.out", "w", stdout);
#endif
register int i,j,cnt=0,s,maxs,ctz;
register mint res=0;
int n=read();
int k=read();
for(i=1;i<W;++i) pw[i]=mint(i).pow(k);
for(i=1;i<=n;++i)
lb.insert(read());
for(i=0;i<W;++i) if(lb.p[i]) pos[cnt++]=i;
if(cnt<=Bb){
maxs=1<<cnt;
for(s=1;s<maxs;++s){
ctz=__builtin_ctz(s);
val[s]=val[s^(1<<ctz)]^lb.p[pos[ctz]];
res+=pw[__builtin_popcountll(val[s])];
}
}else{
for(i=0;i<cnt;++i){
num[i]=lb.p[pos[i]];
for(j=i-1;~j;--j) num[i]|=(num[i]>>(pos[j]+1))<<pos[j];
}
maxs=1<<(W-cnt);
dp[0][0]=1;
for(i=0;i<cnt;++i){
for(s=0;s<maxs;++s){
for(j=0;j<i;++j){
dp[j+1][s^val[i]]+=dp[j][s];
}
}
}
for(i=1;i<=cnt;++i)
for(s=0;s<maxs;++s)
res+=dp[i][s]*(i+__builtin_popcountll(s));
}
print((res*pw2).get());
#ifndef ONLINE_JUDGE
fclose(stdin);
fclose(stdout);
#endif
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3476kb
input:
3 2 1 2 3
output:
12
result:
ok 1 number(s): "12"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3500kb
input:
2 1000000000 1 2
output:
140625003
result:
ok 1 number(s): "140625003"
Test #3:
score: 0
Accepted
time: 1ms
memory: 5516kb
input:
3 4 21 31 15
output:
1076
result:
ok 1 number(s): "1076"
Test #4:
score: 0
Accepted
time: 1ms
memory: 5640kb
input:
4 10 21 16 23 30
output:
3504120
result:
ok 1 number(s): "3504120"
Test #5:
score: 0
Accepted
time: 1ms
memory: 5644kb
input:
5 795325759 23 18 18 15 24
output:
398580583
result:
ok 1 number(s): "398580583"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3476kb
input:
6 425010546 15190825693299 11021868218180 10853490476696 16489831131502 15731786397897 1859285400474
output:
226806798
result:
ok 1 number(s): "226806798"
Test #7:
score: 0
Accepted
time: 1ms
memory: 5580kb
input:
7 376524109 14035202899482 10047025581205 744778190838 10085364176616 17517303536898 10648638998430 4344258259221
output:
909089159
result:
ok 1 number(s): "909089159"
Test #8:
score: 0
Accepted
time: 0ms
memory: 3812kb
input:
8 849112677 12651182249229 2557626671152 16190796268614 7679451552477 1419165382365 16010747922241 1877804892046 6782866140038
output:
60890703
result:
ok 1 number(s): "60890703"
Test #9:
score: 0
Accepted
time: 1ms
memory: 5844kb
input:
9 874735099 10148022499611 4300816040299 6425463859799 11220407430827 16167481816769 5361425691648 9036180330515 1461806017525 5752555300268
output:
371891946
result:
ok 1 number(s): "371891946"
Test #10:
score: 0
Accepted
time: 1ms
memory: 5572kb
input:
10 466547903 14475814446599 10414899512095 8279261110485 15402964537241 12059977291235 14960757658011 15642794803423 176456760404 8544855584093 939455648117
output:
705005476
result:
ok 1 number(s): "705005476"
Test #11:
score: 0
Accepted
time: 1ms
memory: 5840kb
input:
11 587282176 2381973819369 7896756717881 3605049079058 3476202500557 8161539414084 4107261754597 4052905214220 13489145138694 14249896320133 4915388559035 946556082447
output:
221771132
result:
ok 1 number(s): "221771132"
Test #12:
score: 0
Accepted
time: 1ms
memory: 5612kb
input:
12 416671000 12040275816251 17062751464343 7135252213488 464175530141 1680797265108 8088672081270 15974373338891 2807308701611 10474875618229 14385428199760 7217460885705 14772837072591
output:
888526388
result:
ok 1 number(s): "888526388"
Test #13:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
13 555186260 16812780767710 10577402574202 14435021461484 7629604678144 2685467464476 6345623360274 243420234591 10035113157523 3422776077242 10218637237089 14851966122299 403170012001 9905420122107
output:
990043010
result:
ok 1 number(s): "990043010"
Test #14:
score: 0
Accepted
time: 1ms
memory: 3636kb
input:
14 509328299 8353561750434 10104176798819 6443583453798 16526745760567 11644429218948 7613211796505 14675590153019 16014035780673 8977332980184 8018462423140 10321575146167 3765866187251 951943560884 16567591980900
output:
554786244
result:
ok 1 number(s): "554786244"
Test #15:
score: 0
Accepted
time: 0ms
memory: 3848kb
input:
15 608613602 13478763858236 3740903255952 1077573334827 10777446313857 9164622625061 3532139720401 10581691792868 227725402800 1100326438302 11314744041629 5716533742148 13171916589439 3380813371904 4280184438172 3241608634862
output:
451055479
result:
ok 1 number(s): "451055479"
Test #16:
score: 0
Accepted
time: 1ms
memory: 5780kb
input:
16 940201087 10256426323317 3262426443677 11042930351118 9509672586143 6874576733055 17425354233945 44840572217 271060611230 5160013582892 940549858628 3460145241956 1911512043119 6262508016313 15998335209279 4331486722244 1174379722227
output:
609521624
result:
ok 1 number(s): "609521624"
Test #17:
score: 0
Accepted
time: 1ms
memory: 4496kb
input:
17 224938820 17119676032384 14016470814638 9555327895162 4956367760197 14164877522334 11840938437493 196922732084 1117964651219 15662255500985 6799149377748 2081570899516 8101318468846 6806038800783 8481897921532 14327689591834 3468429675406 707483765694
output:
952629882
result:
ok 1 number(s): "952629882"
Test #18:
score: -100
Runtime Error
input:
18 572144592 1034330548675 7466761131151 5479486866730 5805192559012 2072047969997 14094135393106 3957442001455 9636000453501 6359658906102 13786563194342 12655202300227 17497546480004 15210614567784 5757118085432 3507806179905 4092815624732 2831474245754 8905127237409