Python c API, error ld: undefined reference

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I’m trying to compile c code using the python API.

main.c

#define PY_SSIZE_T_CLEAN
#include <Python.h>

int
main(int argc, char *argv[])
{
    PyStatus status;
    PyConfig config;
    PyConfig_InitPythonConfig(&config);
    status = PyConfig_SetBytesString(&config, &config.program_name, argv[0]);
    if (PyStatus_Exception(status)) {
        goto exception;
    }
    status = Py_InitializeFromConfig(&config);
    if (PyStatus_Exception(status)) {
        goto exception;
    }
    PyConfig_Clear(&config);
    PyRun_SimpleString(
        "import sys\n"
        "from time import time,ctime\n"
        "print('Today is', ctime(time()))\n"
    );
    if (Py_FinalizeEx() < 0) {
        exit(120);
    }
    return 0;

  exception:
     PyConfig_Clear(&config);
     Py_ExitStatusException(status);
}

I decided to use gcc for this along with flake

flake.nix

{
  description = "A very basic python c api";

  inputs = {
    nixpkgs.url = "github:nixos/nixpkgs?ref=nixos-unstable";
  };

  outputs = { self, nixpkgs }: 
    let
      system = "x86_64-linux";
      pkgs = import nixpkgs { inherit system; };
    in {
    packages.${system}.default  =
      pkgs.stdenv.mkDerivation {
        name = "hello_python";
        src = self;
        nativeBuildInputs= with pkgs; [
          python313
          gcc
        ];
        buildPhase = ''
          gcc main.c -o hello_python
        '';
        installPhase = ''
          mkdir -p $out/bin; 
          install -t $out/bin hello_python
        '';
        NIX_CFLAGS_COMPILE = [
          "-I${pkgs.python313.outPath}/include/${pkgs.python313.executable}"
        ];
        NIX_LDFLAGS = [
          "-L${pkgs.python313.outPath}/lib"
        ];
      };
  };
}

$ tree
.
├── flake.lock
├── flake.nix
└── main.c

But when I tried to run it, I got a liker error

$ nix run .
error: Cannot build '/nix/store/q0l1ad8a2r0li5w2prhz8kxxvkdhj77q-hello_python.drv'.
       Reason: builder failed with exit code 1.
       Output paths:
         /nix/store/9vbjswb7q3n8csyf428fzdr6yzsk4vxw-hello_python
       Last 20 log lines:
       > Running phase: unpackPhase
       > unpacking source archive /nix/store/navqf7pq5f08byh7kmbq0f84lpm7l7sd-source
       > source root is source
       > Running phase: patchPhase
       > Running phase: updateAutotoolsGnuConfigScriptsPhase
       > Running phase: configurePhase
       > no configure script, doing nothing
       > Running phase: buildPhase
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: /build/ccimUTjq.o: in function `main':
       > main.c:(.text.startup+0x32): undefined reference to `PyConfig_InitPythonConfig'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0x48): undefined reference to `PyConfig_SetBytesString'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0x6a): undefined reference to `PyStatus_Exception'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0x7d): undefined reference to `Py_InitializeFromConfig'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0x9f): undefined reference to `PyStatus_Exception'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0xaf): undefined reference to `PyConfig_Clear'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0xbd): undefined reference to `PyRun_SimpleStringFlags'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0xc2): undefined reference to `Py_FinalizeEx'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0xea): undefined reference to `PyConfig_Clear'
       > /nix/store/dc9vaz50jg7mibk9xvqw5dqv89cxzla3-binutils-2.44/bin/ld: main.c:(.text.startup+0x10c): undefined reference to `Py_ExitStatusException'
       > collect2: error: ld returned 1 exit status
       For full logs, run:
         nix log /nix/store/q0l1ad8a2r0li5w2prhz8kxxvkdhj77q-hello_python.drv

We are looking for an answer in Python - Official NixOS Wiki , C - NixOS Wiki and Cannot link against Python but I didn’t find anything.

Can someone help?