int led_pin = 13;
int btn_pin = 7;

int state = 1;
int old_state;
// 1-state: OFF
// 2-stte:a ON

bool btn_val, btn_old_val;
bool isButtonPressed;

unsigned long currentTime, lastTime;


void setup() {
  pinMode(led_pin, OUTPUT);
  pinMode(btn_pin, INPUT_PULLUP);
}

void loop() {
  currentTime = millis();
  readButton();

  switch (state) {
    case 1: // OFF state
      if (isButtonPressed) {
        state = 2;
      }
      digitalWrite(led_pin, LOW);
      break;

    case 2: // ON state
      if (isButtonPressed || currentTime-lastTime>3000) {
        state = 1;
      }
      digitalWrite(led_pin, HIGH);
      break;
  }

  if (state != old_state) {
    lastTime = currentTime;
  }
  old_state = state;
}

void readButton() {
  btn_val = !digitalRead(btn_pin);

  if (btn_val && !btn_old_val) {
    isButtonPressed = true;
  }
  else {
    isButtonPressed = false;
    delay(50);
  }

  btn_old_val = btn_val;
}