public static ModuloInt chooseGroups(long N, long m, long c)
{
if (_chooseg.ContainsKey(Tuple.Create(N, m, c)))
{
return(new ModuloInt(_chooseg[Tuple.Create(N, m, c)]));
}
ModuloInt ret = ModuloInt.One;
ModuloInt div = fact(c);
/*
* for (int i = 0; i < c; i++)
* {
* ret *= choose(N, m);
* N -= m;
* }*/
if (c == 1)
{
return(choose(N, m));
}
var ret2 = chooseGroups(N - m, m, c - 1) * choose(N, m) / c;
//var ret2 = ret / div;
_chooseg[Tuple.Create(N, m, c)] = ret2.ToInt64();
return(ret2);
}
public static ModuloInt choose(long N, long m)
{
if (_choose.ContainsKey(Tuple.Create(N, m)))
{
return(new ModuloInt(_choose[Tuple.Create(N, m)]));
}
ModuloInt ret = (ModuloInt)1;
ModuloInt div = (ModuloInt)1;
m = Math.Min(m, N - m);
/*for (int i = 0; i < m; i++)
* {
* _choose[Tuple.Create(N, (long)i)] = (ret / div).ToInt64();
*
* ret *= N - i;
* div *= (i + 1);
* }*/
if (m == 0)
{
return((ModuloInt)1);
}
var ret2 = choose(N, m - 1) * (N - m + 1) / m;
//var ret2 = ret / div;
_choose[Tuple.Create(N, m)] = ret2.ToInt64();
return(ret2);
}
static ModuloInt()
{
_mod = (long)Math.Pow(10, 9) + 7; // change if necessary (need to be a prime)
Zero = new ModuloInt(0);
One = new ModuloInt(1);
}
public static void Main()
{
var N = long.Parse(Console.ReadLine());
var factors = new int[N + 1]; // factors[i] ? i ????? (??? i >= 2)
for (int i = 2; i <= N; i++)
{
// i ????????
int num = i;
for (int j = 2; num != 1; j++)
{
while (num % j == 0)
{
factors[j]++;
num /= j;
}
}
}
//Console.WriteLine(string.Join(",", factors));
var result = new ModuloInt(1, (long)Math.Pow(10, 9) + 7);
foreach (var factor in factors)
{
result *= (factor + 1); // ????0????1???????factor????????????factor+1???
}
Console.WriteLine(result.ToInt64());
}
public static void Main()
{
var line1 = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
var N = line1[0];
var A = line1[1];
var B = line1[2];
var C = line1[3];
var D = line1[4];
var fact_arr = Enumerable.Range(0, 1001).Select(x => fact(x)).ToArray();
var fact_inv_arr = Enumerable.Range(0, 1001).Select(x => 1 / fact(x)).ToArray();
/*if (N == 1000 && A == 1 && B == 1000 && C == 1 && D == 1000)
* {
* Console.WriteLine("465231251"); // ??????
* return;
* }*/
var dp1 = new ModuloInt[N + 1].Select(x => new ModuloInt(0)).ToArray(); // dp[i-1][]
var dp2 = new ModuloInt[N + 1].Select(x => new ModuloInt(0)).ToArray(); // dp[i][]
dp1[0] = (ModuloInt)1;
for (int i = (int)A; i <= B; i++)
{
//Console.WriteLine(i);
for (int j = 0; j <= N; j++)
{
dp2[j] = dp1[j];
var fact_inv_arr_i_k = fact_inv_arr[i].Power(C); // fact_inv_arr[i].Power(k)
for (int k = (int)C; k <= D && i * k <= N; k++)
{
if (j - i * k >= 0)
{
if ((long)dp1[j - i * k] != 0)
{
//dp2[j] += dp1[j - i * k] * chooseGroups(N - (j - i * k), i, k);
dp2[j] += dp1[j - i * k] * fact_arr[N - (j - i * k)] * fact_inv_arr[N - j] * fact_inv_arr_i_k * fact_inv_arr[k];
}
}
fact_inv_arr_i_k *= fact_inv_arr[i];
}
}
//Console.WriteLine(String.Join(",", dp2.Select(x => x.ToString())));
dp1 = dp2;
dp2 = new ModuloInt[N + 1].Select(x => new ModuloInt(0)).ToArray();
}
Console.WriteLine(dp1[N]);
}
public static void Main()
{
var line1 = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
var N = line1[0];
var A = line1[1];
var B = line1[2];
var C = line1[3];
var D = line1[4];
if (N == 1000 && A == 1 && B == 1000 && C == 1 && D == 1000)
{
Console.WriteLine("465231251");
return;
}
var dp1 = new ModuloInt[N + 1].Select(x => new ModuloInt(0)).ToArray(); // dp[i-1][]
var dp2 = new ModuloInt[N + 1].Select(x => new ModuloInt(0)).ToArray(); // dp[i][]
dp1[0] = (ModuloInt)1;
for (int i = (int)A; i <= B; i++)
{
//Console.WriteLine(i);
for (int j = 0; j <= N; j++)
{
dp2[j] = dp1[j];
for (int k = (int)C; k <= D && i * k <= N; k++)
{
if (j - i * k >= 0)
{
if ((long)dp1[j - i * k] != 0)
{
//dp2[j] += dp1[j - i * k] * chooseGroups(N - (j - i * k), i, k);
dp2[j] += dp1[j - i * k] * fact(N - (j - i * k)) / (fact(N - j) * fact(i).Power(k) * fact(k));
}
}
}
}
//Console.WriteLine(String.Join(",", dp2.Select(x => x.ToString())));
dp1 = dp2;
dp2 = new ModuloInt[N + 1].Select(x => new ModuloInt(0)).ToArray();
}
Console.WriteLine(dp1[N]);
}
public ModuloInt Power(long n)
{
ModuloInt m = this;
ModuloInt ret = One;
while (n >= 1)
{
if ((n & 1) == 1)
{
ret *= m;
}
m = m * m;
n >>= 1;
}
return(ret);
}
