I'm new in Arduino and today I have a problem with this code:

int led_1 = 10;
int led_2 = 11;
int led_3 = 12;
int button = 3;
int time = 0;
byte val = 0;

void setup() {
  // put your setup code here, to run once:
  pinMode(led_1, OUTPUT);
  pinMode(led_2, OUTPUT);
  pinMode(led_3, OUTPUT);
  pinMode(button, INPUT);
}

void loop() {
  // put your main code here, to run repeatedly:
  val = digitalRead(button);
  
  if (val == HIGH){
    time = millis();
    while (digitalRead(button) == HIGH){
      if (millis() - time < 1000) {digitalWrite(led_1, HIGH);}
      else if (millis() -time > 1000 && millis()-tempo <2000) {digitalWrite(led_2, HIGH);}
      else if (millis()-time >2000) {digitalWrite(led_3, HIGH);}
    }
  }
  else { 
    time =0;
    digitalWrite(led_1, LOW);
    digitalWrite(led_2, LOW);
    digitalWrite(led_3, LOW);
    }
}

The code should works like: If I press the button less then one second, led_1 will turns on. If I press more between one two seconds led_2 will turns on and If I press the button more than 2 seconds led_3 will turns on. If I don't press the button the led remain low. The time variable is used to take the time when I start to press the button and then the control millis()- time should give how long I press the button.

It works for a while, then after a random time (I think) if I push the button, only the led_3 turns on. Why?