feat : add C# solution

202508/2787 numberOfWays/C#/C#.sln

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+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.5.2.0
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "numberOfWays", "numberOfWays.csproj", "{1E81E272-AF2C-9CB4-F90B-0AAC263D10DC}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{1E81E272-AF2C-9CB4-F90B-0AAC263D10DC}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{1E81E272-AF2C-9CB4-F90B-0AAC263D10DC}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{1E81E272-AF2C-9CB4-F90B-0AAC263D10DC}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{1E81E272-AF2C-9CB4-F90B-0AAC263D10DC}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {AD18FC84-E2FB-4382-96DF-8AE7E50C1401}
+	EndGlobalSection
+EndGlobal

202508/2787 numberOfWays/C#/Program.cs

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+// knapsack problem
+public class Solution
+{
+    public int NumberOfWays(int n, int x)
+    {
+        const int MOD = 1_000_000_007;
+        // list all the powers which smaller than n
+        var powers = new List<int>();
+        var num = 1;
+
+        while (true)
+        {
+            int pow = (int)Math.Pow(num, x);
+            if (pow > n)
+                break;
+            powers.Add(pow);
+            num++;
+        }
+
+        // dynamic programming
+        var dp = new int[n + 1];
+        dp[0] = 1;
+
+        foreach (var power in powers)
+        {
+            for (var i = n; i >= power; i--)
+            {
+                dp[i] = (dp[i] + dp[i - power]) % MOD;
+            }
+        }
+
+        return dp[n];
+
+    }
+
+}
+
+class Program
+{
+    static void Main()
+    {
+        var solution = new Solution();
+
+        Console.WriteLine(solution.NumberOfWays(4, 1));
+        Console.WriteLine(solution.NumberOfWays(100, 3));
+
+    }
+}

202508/2787 numberOfWays/C#/numberOfWays.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>Exe</OutputType>
+    <TargetFramework>net8.0</TargetFramework>
+    <ImplicitUsings>enable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+  </PropertyGroup>
+
+</Project>