#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define ssize(x) int(x.size()) #define pb push_back #define mp make_pair #define all(a) begin(a),end(a) // #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define FOR(i, l, r) for(int i = (l); i < (r); ++i) #define FORE(i, l, r) for(int i = (l); i <= (r); ++i) // # define REP(i, n) FOR(i, 0, (n) - 1) # define REP(i, n) FORE(i, 0, (n) - 1) #define FORR(x,arr) for(auto &x: arr) #define REE(s_) {cout<<s_<<'\n';exit(0);} #define GET(arr) for(auto &i: (arr)) sc(i) #define e1 first #define e2 second #define INF 0x7f7f7f7f #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "),...); }(x), cerr << '\n' typedef std::pair<int,int> pi; typedef std::vector<int> vi; typedef std::vector<std::string> vs; typedef int64_t ll; typedef uint64_t ull; using namespace std; using namespace __gnu_pbds; #ifdef ONLINE_JUDGE #define debug(...) {} #endif #ifdef _WIN32 #define getchar_unlocked() _getchar_nolock() #define _CRT_DISABLE_PERFCRIT_LOCKS #endif template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } inline int fstoi(const string &str){auto it=str.begin();bool neg=0;int num=0;if(*it=='-')neg=1;else num=*it-'0';++it;while(it<str.end()) num=num*10+(*it++-'0');if(neg)num*=-1;return num;} inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}} inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}} template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); } template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>; // 1 << 19 if segtree where merges matter. #define N 1000001 constexpr int64_t mod = 1000000007; inline int64_t fastpow(int64_t a, int64_t b){ if(b == 0) return 1; if(b&1){ return (a * fastpow(a,b^1)) % mod; } a = fastpow(a,b >> 1); return (a*a)%mod; } ll fac[N]; ll facinv[N]; // constexpr btw? // -> operation limit that can't be changed by a pragma is too low. (agc051a.cpp tried on pc) void pre(){ fac[0] = 1; FOR(i,1,N) fac[i] = fac[i - 1] * i % mod; if constexpr (mod == 1000000007 && N == 1000001) facinv[N - 1] = 397802501; else facinv[N - 1] = fastpow(fac[N - 1], mod - 2); for(int i = N - 2; i >= 0; --i) facinv[i] = facinv[i + 1] * (i + 1) % mod; // Also i^-1 = facinv[i] * fac[i - 1] (i in 1..n) // Similary idea can be used to get invs of any n numbers in O(n + logp). // -> zamiast *1, *2, *3... do *a[0], *a[1], *a[2]... } ll binom(ll n, ll k){ if(n < k || n < 0) return 0; return fac[n] * facinv[k] % mod * facinv[n - k] % mod; } int main(){ ios_base::sync_with_stdio(0);cin.tie(0); pre(); int n, q; sc(n, q); ll pw2[n + 1]; pw2[0] = 1; FORE(i,1,n) pw2[i] = pw2[i - 1] * 2 % mod; vector<pi> bads; // n == 1 edge. if(n >= 2) bads.push_back({1, 1}); FORE(crn,3,n){ vector<pi> nwbads; FORR(i,bads){ auto tryadd = [&](int f, int s){ if(s < 0 || f < 0) return; if(f > s) swap(f,s); nwbads.emplace_back(f, s); }; tryadd(i.e1 + 2, i.e2 - 1); if(nwbads.size() == 1) break; tryadd(i.e1 - 1, i.e2 + 2); if(nwbads.size() == 1) break; } bads = nwbads; bads.erase(unique(all(bads)), bads.end()); /* debug(crn, bads.size()); */ } /* exit(0); */ sort(all(bads)); /* int pre[3][n + 1]; */ /* REP(md,3){ */ /* pre[md][]; */ /* } */ /* debug(bads); */ string s; getstr(s); int mdcnts[2]{}; int cnt[128]{}; int it = 0; FORR(i,s){ ++cnt[i]; // rip jane street if(i == 'C'){ ++mdcnts[it & 1]; } else if(i == 'Z'){ ++mdcnts[(it ^ 1) & 1]; } ++it; } // EZZZZZZZZZZ clutch 1h przed końcem. // (rozpisanie binomial coeffów trzeba zachować na ostateczność, wcześniej można tylko googlować) ll sums[n+1][3]; sums[0][0] = 1; sums[0][1] = 0; sums[0][2] = 0; FORE(i,1,n){ REP(x,3){ sums[i][x] = sums[i - 1][x] + sums[i - 1][(x - 1 + 3) % 3]; sums[i][x] %= mod; /* debug(i, x, sums[i][x]); */ } } int whcmod = bads[0].e1 % 3; // yes jane street. auto calc_res = [&](){ if(n == 1){ return (long ) (1 + (s[0] == 'N')); } ll res = 0; res = pw2[cnt['N']]; REP(ile,cnt['N'] + 1){ /* pi wh = {cnt['C'] + ile, cnt['Z'] + cnt['N'] - ile}; */ /* if(wh.e1 > wh.e2) */ /* swap(wh.e1, wh.e2); */ /* if(binary_search(all(bads), wh)){ */ /* /1* debug(ile); *1/ */ /* /1* res -= binom(cnt['N'], ile); *1/ */ /* res -= sums[cnt['N']][ile % 3]; */ /* break; */ /* } */ /* int sthhhh = whcmod - cnt['C']; */ // EZZZZZZZZZZZZZZZZZZZZZZZZZZZZ. // Zakomentowanie 10 linijek i dodanie trzech to obtain the speeed. // Like it's 2020. int sthhhh = bads[0].e1 - cnt['C']; sthhhh %= 3; sthhhh += 3; sthhhh %= 3; res -= sums[cnt['N']][sthhhh % 3]; break; } pi sth = {n / 2, n / 2}; if(sth.e1 + sth.e2 < n) ++sth.e2; assert(sth.e1 + sth.e2 == n); // Czej WTF. how is that not bugged? // -> somehow jak breakuje po pierwszym, to zawsze mam closest do siebie, ale fart xddddd. if(!binary_search(all(bads), sth)){ res -= mdcnts[0] == 0; res -= mdcnts[1] == 0; } /* REP(_,2){ */ /* FORR(i,bads){ */ /* res -= binom(cnt['N'], ); */ /* } */ /* swap(cnt['C'], cnt['Z']); */ /* } */ res %= mod; res += mod; res %= mod; return res; }; cout << calc_res() << '\n'; while(q--){ int wh; char c; sc(wh); getch(c); --wh; int it = wh; --cnt[s[wh]]; char i = s[wh]; // rip jane street if(i == 'C'){ --mdcnts[it & 1]; } else if(i == 'Z'){ --mdcnts[(it ^ 1) & 1]; } s[wh] = c; i = s[wh]; // rip jane street if(i == 'C'){ ++mdcnts[it & 1]; } else if(i == 'Z'){ ++mdcnts[(it ^ 1) & 1]; } ++cnt[s[wh]]; cout << calc_res() << '\n'; } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 | #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define ssize(x) int(x.size()) #define pb push_back #define mp make_pair #define all(a) begin(a),end(a) // #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define FOR(i, l, r) for(int i = (l); i < (r); ++i) #define FORE(i, l, r) for(int i = (l); i <= (r); ++i) // # define REP(i, n) FOR(i, 0, (n) - 1) # define REP(i, n) FORE(i, 0, (n) - 1) #define FORR(x,arr) for(auto &x: arr) #define REE(s_) {cout<<s_<<'\n';exit(0);} #define GET(arr) for(auto &i: (arr)) sc(i) #define e1 first #define e2 second #define INF 0x7f7f7f7f #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "),...); }(x), cerr << '\n' typedef std::pair<int,int> pi; typedef std::vector<int> vi; typedef std::vector<std::string> vs; typedef int64_t ll; typedef uint64_t ull; using namespace std; using namespace __gnu_pbds; #ifdef ONLINE_JUDGE #define debug(...) {} #endif #ifdef _WIN32 #define getchar_unlocked() _getchar_nolock() #define _CRT_DISABLE_PERFCRIT_LOCKS #endif template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } inline int fstoi(const string &str){auto it=str.begin();bool neg=0;int num=0;if(*it=='-')neg=1;else num=*it-'0';++it;while(it<str.end()) num=num*10+(*it++-'0');if(neg)num*=-1;return num;} inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}} inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}} template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); } template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>; // 1 << 19 if segtree where merges matter. #define N 1000001 constexpr int64_t mod = 1000000007; inline int64_t fastpow(int64_t a, int64_t b){ if(b == 0) return 1; if(b&1){ return (a * fastpow(a,b^1)) % mod; } a = fastpow(a,b >> 1); return (a*a)%mod; } ll fac[N]; ll facinv[N]; // constexpr btw? // -> operation limit that can't be changed by a pragma is too low. (agc051a.cpp tried on pc) void pre(){ fac[0] = 1; FOR(i,1,N) fac[i] = fac[i - 1] * i % mod; if constexpr (mod == 1000000007 && N == 1000001) facinv[N - 1] = 397802501; else facinv[N - 1] = fastpow(fac[N - 1], mod - 2); for(int i = N - 2; i >= 0; --i) facinv[i] = facinv[i + 1] * (i + 1) % mod; // Also i^-1 = facinv[i] * fac[i - 1] (i in 1..n) // Similary idea can be used to get invs of any n numbers in O(n + logp). // -> zamiast *1, *2, *3... do *a[0], *a[1], *a[2]... } ll binom(ll n, ll k){ if(n < k || n < 0) return 0; return fac[n] * facinv[k] % mod * facinv[n - k] % mod; } int main(){ ios_base::sync_with_stdio(0);cin.tie(0); pre(); int n, q; sc(n, q); ll pw2[n + 1]; pw2[0] = 1; FORE(i,1,n) pw2[i] = pw2[i - 1] * 2 % mod; vector<pi> bads; // n == 1 edge. if(n >= 2) bads.push_back({1, 1}); FORE(crn,3,n){ vector<pi> nwbads; FORR(i,bads){ auto tryadd = [&](int f, int s){ if(s < 0 || f < 0) return; if(f > s) swap(f,s); nwbads.emplace_back(f, s); }; tryadd(i.e1 + 2, i.e2 - 1); if(nwbads.size() == 1) break; tryadd(i.e1 - 1, i.e2 + 2); if(nwbads.size() == 1) break; } bads = nwbads; bads.erase(unique(all(bads)), bads.end()); /* debug(crn, bads.size()); */ } /* exit(0); */ sort(all(bads)); /* int pre[3][n + 1]; */ /* REP(md,3){ */ /* pre[md][]; */ /* } */ /* debug(bads); */ string s; getstr(s); int mdcnts[2]{}; int cnt[128]{}; int it = 0; FORR(i,s){ ++cnt[i]; // rip jane street if(i == 'C'){ ++mdcnts[it & 1]; } else if(i == 'Z'){ ++mdcnts[(it ^ 1) & 1]; } ++it; } // EZZZZZZZZZZ clutch 1h przed końcem. // (rozpisanie binomial coeffów trzeba zachować na ostateczność, wcześniej można tylko googlować) ll sums[n+1][3]; sums[0][0] = 1; sums[0][1] = 0; sums[0][2] = 0; FORE(i,1,n){ REP(x,3){ sums[i][x] = sums[i - 1][x] + sums[i - 1][(x - 1 + 3) % 3]; sums[i][x] %= mod; /* debug(i, x, sums[i][x]); */ } } int whcmod = bads[0].e1 % 3; // yes jane street. auto calc_res = [&](){ if(n == 1){ return (long ) (1 + (s[0] == 'N')); } ll res = 0; res = pw2[cnt['N']]; REP(ile,cnt['N'] + 1){ /* pi wh = {cnt['C'] + ile, cnt['Z'] + cnt['N'] - ile}; */ /* if(wh.e1 > wh.e2) */ /* swap(wh.e1, wh.e2); */ /* if(binary_search(all(bads), wh)){ */ /* /1* debug(ile); *1/ */ /* /1* res -= binom(cnt['N'], ile); *1/ */ /* res -= sums[cnt['N']][ile % 3]; */ /* break; */ /* } */ /* int sthhhh = whcmod - cnt['C']; */ // EZZZZZZZZZZZZZZZZZZZZZZZZZZZZ. // Zakomentowanie 10 linijek i dodanie trzech to obtain the speeed. // Like it's 2020. int sthhhh = bads[0].e1 - cnt['C']; sthhhh %= 3; sthhhh += 3; sthhhh %= 3; res -= sums[cnt['N']][sthhhh % 3]; break; } pi sth = {n / 2, n / 2}; if(sth.e1 + sth.e2 < n) ++sth.e2; assert(sth.e1 + sth.e2 == n); // Czej WTF. how is that not bugged? // -> somehow jak breakuje po pierwszym, to zawsze mam closest do siebie, ale fart xddddd. if(!binary_search(all(bads), sth)){ res -= mdcnts[0] == 0; res -= mdcnts[1] == 0; } /* REP(_,2){ */ /* FORR(i,bads){ */ /* res -= binom(cnt['N'], ); */ /* } */ /* swap(cnt['C'], cnt['Z']); */ /* } */ res %= mod; res += mod; res %= mod; return res; }; cout << calc_res() << '\n'; while(q--){ int wh; char c; sc(wh); getch(c); --wh; int it = wh; --cnt[s[wh]]; char i = s[wh]; // rip jane street if(i == 'C'){ --mdcnts[it & 1]; } else if(i == 'Z'){ --mdcnts[(it ^ 1) & 1]; } s[wh] = c; i = s[wh]; // rip jane street if(i == 'C'){ ++mdcnts[it & 1]; } else if(i == 'Z'){ ++mdcnts[(it ^ 1) & 1]; } ++cnt[s[wh]]; cout << calc_res() << '\n'; } } |