Language: C++

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,k,n) for(int i = (int)(k); i < (int)(n); i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) a.begin(), a.end()
#define MS(m,v) memset(m,v,sizeof(m))
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<string> vs;
typedef pair<int, int> pii;
const int MOD = 1000000007;
const int INF = MOD + 1;
const ld EPS = 1e-12;
template<class T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<class T> T &chmax(T &a, const T &b) { return a = max(a, b); }

/*--------------------template--------------------*/


typedef ld Data;
typedef vector<Data> Array;
typedef vector<Array> Matrix;

bool is_zero(Data dat) { return (abs(dat) < EPS); }

Matrix operator-(Matrix mat) {
	REP(i, mat.size()) REP(j, mat[0].size()) mat[i][j] = -mat[i][j];
	return mat;
}

Matrix operator+(Matrix lhs, const Matrix &rhs) {
	REP(i, lhs.size()) REP(j, lhs[0].size()) lhs[i][j] = lhs[i][j] + rhs[i][j];
	return lhs;
}

Matrix operator-(Matrix lhs, const Matrix &rhs) {
	REP(i, lhs.size()) REP(j, lhs[0].size()) lhs[i][j] = lhs[i][j] - rhs[i][j];
	return lhs;
}

Matrix operator*(const Matrix &lhs, const Matrix &rhs) {
	Matrix res(lhs.size(), Array(rhs[0].size(), 0));
	REP(i, lhs.size()) REP(j, rhs[0].size()) REP(k, rhs.size())
		res[i][j] = fma(lhs[i][k], rhs[k][j], res[i][j]);
	return res;
}

Array operator+(const Array &lhs, const Array &rhs) {
	Array res = lhs;
	REP(i, rhs.size()) res[i] = res[i] + rhs[i];
	return res;
}

Array operator*(const Matrix &lhs, const Array &rhs) {
	Array res(lhs.size());
	REP(i, lhs.size())
		res[i] = inner_product(begin(lhs[i]), end(lhs[i]), begin(rhs), Data(0));
	return res;
}

Array operator*(Data scalar, const Array &rhs) {
	Array res(rhs.size());
	REP(i, rhs.size())
		res[i] = scalar * rhs[i];
	return res;
}

Matrix transpose(const Matrix &A) {
	const int n = A[0].size(), m = A.size();
	Matrix res(n, Array(m, 0));
	REP(i, n)REP(j, m) res[i][j] = A[j][i];
	return res;
}

Data inner_product_ex(const Array& a, const Array& b, const Matrix& m) {
	Array b_prime = m*b;
	return inner_product(begin(a), end(a), begin(b_prime), Data(0));
}

Data norm(const Array &a) {
	return inner_product(begin(a), end(a), begin(a), Data(0));
}

Data norm(const Array &a, const Matrix &M) {
	return inner_product_ex(a, a, M);
}

int rankMat(Matrix A) {
	const int n = A.size(), m = A[0].size();
	int r = 0;
	for (int i = 0; r < n && i < m; ++i) {
		int pivot = r;
		for (int j = r + 1; j < n; ++j)
			if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
		swap(A[pivot], A[r]);
		if (is_zero(A[r][i])) continue;
		for (int k = m - 1; k >= i; --k)
			A[r][k] = A[r][k] / A[r][i];
		for (int j = r + 1; j < n; ++j)
			for (int k = m - 1; k >= i; --k)
				A[j][k] = fma(-A[r][k], A[j][i], A[j][k]);
		++r;
	}
	return r;
}

Data det(Matrix A) {
	const int n = A.size();
	Data D = Data(1);
	for (int i = 0; i < n; ++i) {
		int pivot = i;
		for (int j = i + 1; j < n; ++j)
			if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
		swap(A[pivot], A[i]);
		D = D * A[i][i] * Data(i != pivot ? -1 : 1);
		if (is_zero(A[i][i])) break;
		for (int j = i + 1; j < n; ++j)
			for (int k = n - 1; k >= i; --k)
				A[j][k] = A[j][k] - A[i][k] * A[j][i] / A[i][i];
	}
	return D;
}

Array gauss_jordan(const Matrix& A, const Array& b)
{
	int n = A.size();
	Matrix B(n, Array(n + 1));
	REP(i, n)REP(j, n) B[i][j] = A[i][j];
	REP(i, n) B[i][n] = b[i];
	REP(i, n)
	{
		int pivot = i;
		FOR(j, i, n)
		{
			if (abs(B[j][i]) > abs(B[pivot][i])) pivot = j;
		}
		swap(B[i], B[pivot]);

		if (abs(B[i][i]) < EPS) return Array();
		FOR(j, i + 1, n + 1) B[i][j] /= B[i][i];
		REP(j, n)
		{
			if (i != j)
			{
				FOR(k, i + 1, n + 1) B[j][k] -= B[j][i] * B[i][k];
			}
		}
	}
	Array x(n);
	REP(i, n) x[i] = B[i][n];
	return x;
}

int main()
{
	cin.sync_with_stdio(false); cout << fixed << setprecision(10);
	REP(i, 111111) dp[i] = 0;
	int s, n, k;
	cin >> s >> n >> k;
	s = abs(s);
	if (n == 1)
	{
		cout << s / k << endl;
		return 0;
	}
	ld adv[11][111];
	MS(adv, 0);
	adv[0][0] = 1.0;
	REP(i, k)
	{
		REP(j, 100)
		{
			FOR(dice, 1, n + 1)
			{
				adv[i + 1][j + dice] += adv[i][j] / n;
			}
		}
	}
	vector<ld> v;
	REP(i, 101) v.push_back(adv[k][i]);
	ld exp = 0;
	REP(i, 111) exp += i*adv[k][i];
	ld ans = 0;
	if (s > 100000)
	{
		ans += (s - 100000) / exp;
		s = 100000;
	}
	mx = n*k;
	Matrix A(mx, Array(mx));
	Array b(mx);
	A[0][0] = 1;
	FOR(i, 1, mx)
	{
		FOR(j, 1, mx+1)
		{
			A[i][abs(i-j)] += v[j];
		}
	}
	FOR(i, 1, mx)
	{
		A[i][i] -= 1;
		b[i] = -1;
	}
	Array x = gauss_jordan(A, b);
	REP(i, mx) dp[i] = x[i];
	FOR(i, mx, s + 1)
	{
		REP(j, 101)
		{
			if (i - j < 0) break;
			dp[i] += dp[i - j] * v[j];
		}
		dp[i] += 1;
	}
	cout << dp[s] + ans << endl;
	return 0;
}

Compiler output:
a.cc: In function 'int main()':
a.cc:158:24: error: 'dp' was not declared in this scope; did you mean 'dup'?
  158 |         REP(i, 111111) dp[i] = 0;
      |                        ^~
      |                        dup
a.cc:190:9: error: 'mx' was not declared in this scope
  190 |         mx = n*k;
      |         ^~
a.cc:207:20: error: 'dp' was not declared in this scope; did you mean 'dup'?
  207 |         REP(i, mx) dp[i] = x[i];
      |                    ^~
      |                    dup
a.cc:213:25: error: 'dp' was not declared in this scope; did you mean 'dup'?
  213 |                         dp[i] += dp[i - j] * v[j];
      |                         ^~
      |                         dup
a.cc:215:17: error: 'dp' was not declared in this scope; did you mean 'dup'?
  215 |                 dp[i] += 1;
      |                 ^~
      |                 dup
a.cc:217:17: error: 'dp' was not declared in this scope; did you mean 'dup'?
  217 |         cout << dp[s] + ans << endl;
      |                 ^~
      |                 dup