#include #define EPS 1e-9 #define INF 1070000000LL #define MOD 1000000007LL #define fir first #define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++) #define numa(x,a) for(auto x: a) #define ite iterator #define mp make_pair #define rep(i,n) rep2(i,0,n) #define rep2(i,m,n) for(int i=m;i<(n);i++) #define pb push_back #define pf push_front #define sec second #define sz(x) ((int)(x).size()) #define ALL( c ) (c).begin(), (c).end() #define gcd(a,b) __gcd(a,b) #define mem(x,n) memset(x,n,sizeof(x)) #define endl "\n" using namespace std; template void deploy(std::ostream &os, const TUPLE &tuple){} template void deploy(std::ostream &os, const TUPLE &t){ os << (POS == 0 ? "" : ", ") << get(t); deploy(os, t); } template std::ostream& operator<<(std::ostream &os, std::pair &p){ os << "(" << p.first <<", " << p.second <<")";return os; } template std::ostream& operator<<(std::ostream &os, std::vector &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; } template std::ostream& operator<<(std::ostream &os, std::set &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; } template std::ostream& operator<<(std::ostream &os, std::map &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os << "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "}" : ", "); return os; } #define DEBUG1(var0) { std::cerr << (#var0) << "=" << (var0) << endl; } #define DEBUG2(var0, var1) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG1(var1); } #define DEBUG3(var0, var1, var2) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG2(var1,var2); } #define DEBUG4(var0, var1, var2, var3) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG3(var1,var2,var3); } using ll = long long; int N,S,K; ll memo[110][20010]; ll dp_go(int now, int sum){ if (sum > S) { return -2; } if (now == N){ if (sum == S) { return 1; } return -2; } if (memo[now][sum] >= 0) { return memo[now][sum]; } if (memo[now][sum] == -2) { return -1; } ll ans = 0; bool OK = false; int remain = N - now; for (int x = 0; sum + x <= S; x+=remain) { int y = dp_go(now+1, sum + x); if (y != -2) { OK = true; ans += y; ans %= MOD; } } if (OK) { return memo[now][sum] = ans; }else{ return memo[now][sum] = -2; } } int main() { cin.tie(0); ios_base::sync_with_stdio(0); mem(memo,-1); cin >> N >> S >> K; rep(i,N){ S -= i * K; } if (S < 0) { cout << 0 << endl; return 0; } DEBUG1(S); cout << max(0LL, dp_go(0,0)) << endl; return 0; }