n, a, b = map(int, input().split())
P = 10 ** 9 + 7
def inv(x): return pow(x, P - 2, P)
A = a * inv(a + b)
B = b * inv(a + b)
C = a * inv(b)
f = [[0] * 1005 for i in range(1005)]
for i in range(n, 0, -1):
for j in range(n - 1, -1, -1):
if(i + j >= n): f[i][j] = (i + j + C) % P
else: f[i][j] = (A * f[i + 1][j] + B * f[i][j + i]) % P
print(f[1][0])
#include <bits/stdc++.h>
#define ff first
#define ss second
#define ll long long
#define ld long double
#define pb push_back
#define mp make_pair
#define sws ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define endl '\n'
#define teto(a, b) ((a+b-1)/(b))
using namespace std;
// Extra
#define all(x) x.begin(), x.end()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//
const int MAX = 300010;
const ll MOD = (int)1e9 +7;
const int INF = 1e9;
const ll LLINF = 0x3f3f3f3f3f3f3f3f;
const ld EPS = 1e-8;
ll fexp(ll b, ll e) {
if(e == 0) return 1;
ll res = fexp(b, e/2);
res = (res * res) % MOD;
if(e%2) res = (res * b) % MOD;
return res;
}
ll inv(ll a) {
return fexp(a, MOD-2);
}
ll k, pa, pb;
ll tab[2002][2002];
ll ipapb;
ll dp(int qa, int s) {
if(qa >= s) {
ll p = (pa * ipapb) % MOD;
return (qa + p*inv(MOD + 1-p)) % MOD;
}
if(s <= 0) {
return 0;
}
if(tab[qa][s] != -1) return tab[qa][s];
ll pegaa = (dp(qa+1, s) * pa) % MOD;
pegaa = (pegaa * ipapb) % MOD;
ll pegab = ((qa + dp(qa, s-qa)) * pb) % MOD;
pegab = (pegab * ipapb) % MOD;
ll res = (pegaa + pegab) % MOD;
return tab[qa][s] = res;
}
int main() {
sws;
memset(tab, -1, sizeof(tab));
cin >> k >> pa >> pb;
ipapb = inv(pa + pb);
cout << dp(1, k) << endl;
return 0;
}467B - Fedor and New Game | 252C - Points on Line |
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