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- typedef int64_t ll;
- typedef long long ll;
- typedef pair<ll,ll> lll;
- typedef pair<ll,int> lli;
- typedef pair<int,int> ii;
- #define EL printf("\n")
- #define OK printf("OK")
- #define pb push_back
- #define mp make_pair
- #define ep emplace_back
- #define X first
- #define Y second
- #define fillchar(a,x) memset(a, x, sizeof(a))
- #define FOR(i,l,r) for (int i=l;i<=r;i++)
- #define FORD(i,r,l) for (int i=r;i>=l;i--)
- const int base = 1e9;
- typedef vector<int> BigInt;
- void Set(BigInt &a) {
- while (a.size() > 1 && a.back() == 0) a.pop_back();
- }
- BigInt Integer(string s) {
- BigInt ans;
- if (s[0] == '-') return ans;
- if (s.size() == 0) {ans.pb(0); return ans;}
- while (s.size()%9 != 0) s = '0'+s;
- for (int i=0;i<s.size();i+=9) {
- int v = 0;
- for (int j=i;j<i+9;j++) v = v*10+(s[j]-'0');
- ans.insert(ans.begin(),v);
- }
- Set(ans);
- return ans;
- }
- BigInt Integer(char c[]) {
- string s = "";
- FOR(i,0,strlen(c)-1) s = s + c[i];
- return Integer(s);
- }
- BigInt Integer(ll x) {
- string s = "";
- while (x > 0) s = char(x%10+'0') + s, x /= 10;
- return Integer(s);
- }
- BigInt Integer(int x) {
- return Integer((ll) x);
- }
- istream & operator >> (istream &in, BigInt &a) {
- char ch[10001];
- in >> ch;
- a = Integer(ch);
- return in;
- }
- ostream & operator << (ostream &out, BigInt a) {
- Set(a);
- out << ((a.size() == 0) ? 0 : a.back());
- FORD(i,a.size()-2,0) out<<setfill('0') << setw(9)<<a[i];
- return out;
- }
- bool operator < (BigInt a, BigInt b) {
- Set(a);
- Set(b);
- if (a.size() != b.size()) return (a.size() < b.size());
- FORD(i,a.size()-1,0)
- if (a[i] != b[i]) return (a[i] < b[i]);
- return false;
- }
- bool operator > (BigInt a, BigInt b) {
- return (b < a);
- }
- bool operator == (BigInt a, BigInt b) {
- return (!(a < b) && !(b < a));
- }
- bool operator <= (BigInt a, BigInt b) {
- return (a < b || a == b);
- }
- bool operator >= (BigInt a, BigInt b) {
- return (b < a || b == a);
- }
- bool operator < (BigInt a, int b) {
- return (a < Integer(b));
- }
- bool operator > (BigInt a, int b) {
- return (a > Integer(b));
- }
- bool operator == (BigInt a, int b) {
- return (a == Integer(b));
- }
- bool operator >= (BigInt a, int b) {
- return (a >= Integer(b));
- }
- bool operator <= (BigInt a, int b) {
- return (a <= Integer(b));
- }
- BigInt max(BigInt a, BigInt b) {
- if (a > b) return a;
- return b;
- }
- BigInt min(BigInt a, BigInt b) {
- if (a < b) return a;
- return b;
- }
- BigInt operator + (BigInt a, BigInt b) {
- Set(a);
- Set(b);
- BigInt ans;
- int carry = 0;
- FOR(i,0,max(a.size(), b.size())-1) {
- if (i < a.size()) carry += a[i];
- if (i < b.size()) carry += b[i];
- ans.pb(carry%base);
- carry /= base;
- }
- if (carry) ans.pb(carry);
- Set(ans);
- return ans;
- }
- BigInt operator + (BigInt a, int b) {
- return a + Integer(b);
- }
- BigInt operator ++ (BigInt &a) { // ++a
- a = a + 1;
- return a;
- }
- void operator += (BigInt &a, BigInt b) {
- a = a + b;
- }
- void operator += (BigInt &a, int b) {
- a = a + b;
- }
- BigInt operator - (BigInt a, BigInt b) {
- Set(a);
- Set(b);
- BigInt ans;
- int carry = 0;
- FOR(i,0,a.size()-1) {
- carry += a[i] - (i < b.size() ? b[i] : 0);
- if (carry < 0) ans.pb(carry+base), carry = -1;
- else ans.pb(carry), carry = 0;
- }
- Set(ans);
- return ans;
- }
- BigInt operator - (BigInt a, int b) {
- return a - Integer(b);
- }
- void operator -- (BigInt &a) { // --a
- a = a - 1;
- }
- void operator -= (BigInt &a, BigInt b) {
- a = a + b;
- }
- void operator -= (BigInt &a, int b) {
- a = a - b;
- }
- BigInt operator * (BigInt a, BigInt b) {
- Set(a);
- Set(b);
- BigInt ans;
- ans.assign(a.size()+b.size(), 0);
- FOR(i,0,a.size()-1) {
- ll carry = 0ll;
- for (int j=0;j<b.size() || carry > 0;j++) {
- ll s = ans[i+j] + carry + (ll)a[i]*(j<b.size()?(ll)b[j]:0ll);
- ans[i+j] = s%base;
- carry = s/base;
- }
- }
- Set(ans);
- return ans;
- }
- BigInt operator * (BigInt a, int b) {
- return a * Integer(b);
- }
- void operator *= (BigInt &a, BigInt b) {
- a = a * b;
- }
- void operator *= (BigInt &a, int b) {
- a = a * b;
- }
- BigInt operator / (BigInt a, BigInt b) {
- Set(a);
- Set(b);
- if (b == Integer(0)) return Integer("-1");
- BigInt ans, cur;
- FORD(i,a.size()-1,0) {
- cur.insert(cur.begin(), a[i]);
- int x = 0, L = 0, R = base;
- while (L <= R) {
- int mid = (L+R)>>1;
- if (b*Integer(mid) > cur) {
- x = mid;
- R = mid-1;
- }
- else
- L = mid+1;
- }
- cur = cur - Integer(x-1)*b;
- ans.insert(ans.begin(),x-1);
- }
- Set(ans);
- return ans;
- }
- BigInt operator / (BigInt a, int b) {
- Set(a);
- BigInt ans;
- ll cur = 0ll;
- FORD(i,a.size()-1,0) {
- cur = (cur*(ll)base + (ll)a[i]);
- ans.insert(ans.begin(),cur/b);
- cur %= b;
- }
- Set(ans);
- return ans;
- }
- void operator /= (BigInt &a, BigInt b) {
- a = a / b;
- }
- void operator /= (BigInt &a, int b) {
- a = a / b;
- }
- BigInt operator % (BigInt a, BigInt b) {
- Set(a);
- Set(b);
- if (b == Integer(0)) return Integer("-1");
- BigInt ans;
- FORD(i,a.size()-1,0) {
- ans.insert(ans.begin(), a[i]);
- int x = 0, L = 0, R = base;
- while (L <= R) {
- int mid = (L+R)>>1;
- if (b*Integer(mid) > ans) {
- x = mid;
- R = mid-1;
- }
- else
- L = mid+1;
- }
- ans = ans - Integer(x-1)*b;
- }
- Set(ans);
- return ans;
- }
- BigInt operator % (BigInt a, int b) {
- Set(a);
- if (b == 0) return Integer(-1);
- return a-(a/b)*b;
- }
- void operator %= (BigInt &a, BigInt b) {
- a = a % b;
- }
- void operator %= (BigInt &a, int b) {
- a = a % Integer(b);
- }
- BigInt gcd(BigInt a, BigInt b) {
- Set(a);
- Set(b);
- while (b > Integer(0)) {
- BigInt r = a%b;
- a = b;
- b = r;
- }
- Set(a);
- return a;
- }
- BigInt lcm(BigInt a, BigInt b) {
- return (a*b/gcd(a,b));
- }
- BigInt sqrt(BigInt a) {
- BigInt x0 = a, x1 = (a+1)/2;
- while (x1 < x0) {
- x0 = x1;
- x1 = (x1+a/x1)/2;
- }
- return x0;
- }
- BigInt pow(BigInt a, BigInt b) {
- if (b == Integer(0)) return Integer(1);
- BigInt tmp = pow(a, b/2);
- if (b%2 == 0) return tmp * tmp;
- return tmp * tmp * a;
- }
- BigInt pow(BigInt a, int b) {
- return pow(a,(Integer(b)));
- }
- int log(int n, BigInt a) {
- Set(a);
- int ans = 0;
- while (a > Integer(1)) {
- ans++;
- a /= n;
- }
- return ans;
- }
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