Submission #19475

#	Time	Username	Problem	Language	Result	Execution time	Memory
19475		emppu	Ω (kriii4_P3)	C++14	100 / 100	0 ms	1724 KiB

P3

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>

#include <algorithm>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <deque>
#include <list>
#include <bitset>
#include <tuple>

using namespace std;

#define f0(_X,_Y) for(int (_X)=0;(_X)<(_Y);++(_X))
#define f1(_X,_Y) for(int (_X)=1;(_X)<=(_Y);++(_X))
#define ff(_X,_Y,_Z) for(int (_X)=(_Y);(_X)<=(_Z);++(_X))
#define fF(_X,_Y,_Z) for(int (_X)=(_Y);(_X)<(_Z);++(_X))
#define rf0(_X,_Y) for(int _X=(_Y)-1;(_X)>=0;--(_X))
#define rf1(_X,_Y) for(int _X=(_Y);(_X)>0;--(_X))
#define rff(_X,_Y,_Z) for(int _X=(_Y);(_X)>=(_Z);--(_X))
#define rfF(_X,_Y,_Z) for(int _X=(_Y);(_X)>(_Z);--(_X))
#define PRT(_X) std::cout<< #_X ": "<<_X<<std::endl;

#define scan1(_X) scanf("%d",&_X);
#define scan2(_X,_Y) scanf("%d%d",&_X,&_Y);
#define scan3(_X,_Y,_Z) scanf("%d%d%d",&_X,&_Y,&_Z);
#define define1(_1) int _1; scan1(_1)
#define define2(_1,_2) int _1,_2; scan2(_1,_2)
#define define3(_1,_2,_3) int _1,_2,_3; scan3(_1,_2,_3)
#define EXPAND(_1) _1
#define SELECT(_1,_2,_3,_4,NAME,...) NAME
#define scan(...) EXPAND(SELECT(__VA_ARGS__, scan4, scan3, scan2, scan1)(__VA_ARGS__))
#define define(...) EXPAND(SELECT(__VA_ARGS__, define4, define3, define2, define1)(__VA_ARGS__))
#define print(_X) printf("%d\n",_X)
#define PAIR_STRUCT(_T,_X,_Y,...) struct _T{int _X,_Y,##__VA_ARGS__; bool friend operator < (const _T &p, const _T &q){if(p._X!=q._X) return p._X<q._X; return p._Y<q._Y;}}

typedef long long ll;
const int MOD = 1000000007;
ll a[103];
ll d[103];

ll inv(ll a, ll b=MOD)
{
	a %= MOD;
	if(a<0) a+=MOD;
	ll s = 0;  ll  old_s = 1;
	ll r = b;  ll  old_r = a;
	while (r!=0)
	{
		ll quotient = old_r / r;
		tie(old_r, r) = make_tuple(r, old_r - quotient * r);
		tie(old_s, s) = make_tuple(s, old_s - quotient * s);
	}
	ll inv = old_s%MOD;
	if(inv<0) inv += MOD;
	return inv;
}

int main()
{
	ll p,q,n,k;
	scanf("%lld%lld%lld%lld",&p,&q,&n,&k);

	ll Pl = q*inv(p)%MOD;
	ll Pr = (p-q)*inv(p)%MOD;

	if(k==0)
		print(0);
	else if(k==n)
		print(1);
	else if(n==2)
	{
		printf("%lld\n",Pr);
	}
	else
	{
		if(q==0)
			print(1);
		else if(q==p)
			print(0);
		else
		{
			a[1] = 1;
			a[2] = inv(Pr);
			ff(i,2,n-2) // d_i = a[i] d_1
			{
				// d[i] = Pl d[i-1] + Pr d[i+1]
				// d[i+1] = (a[i] - Pl a[i-1] )/Pr d_1
				a[i+1] = (a[i]-Pl*a[i-1]%MOD)*inv(Pr)%MOD;
				if(a[i+1]<0) a[i+1] += MOD;
			}

			// d[n-1] = a[n-1] d_1
			// d[n-1] = Pl a[n-2] d_1 + Pr
			// d_1 = Pr / (a[n-1]-Pl a[n-2])
			d[1] = Pr * inv(a[n-1]-Pl*a[n-2]%MOD) % MOD;
			if(d[1]<0) d[1] += MOD;
			printf("%lld\n",d[1]*a[k]%MOD);
		}
	}
	return 0;
}

• Subtask 1: 100 / 100