Why does my code not works? (Arduino language)

Question

This is my code

#define BUTL 13
#define BUTR 12
#define BUTC 11
#define LEDL 3
#define LEDR 2
bool R = false;
bool L = false;

void setup() {
// put your setup code here, to run once:
pinMode(BUTL, INPUT_PULLUP);
pinMode(BUTR, INPUT_PULLUP);
pinMode(LEDL, OUTPUT);
pinMode(LEDR, OUTPUT);
digitalWrite(LEDL, LOW);
digitalWrite(LEDR, LOW);
}

void loop() {
// put your main code here, to run repeatedly:
if (digitalRead(BUTR)){
R = !R;
}
if (digitalRead(BUTL)){
L = !L;
}
if (digitalRead(BUTC)){
if (L == R){
L = !L;
R = !R;
} else {
L = R = false;
}
}
if (millis() % 1000 >= 0){
if (L){
digitalWrite(LEDL, HIGH);
}
if (R){
digitalWrite(LEDR, HIGH);
}
}
if (millis() % 1000 >= 500){
if (L){
digitalWrite(LEDL, LOW);
}
if (R){
digitalWrite(LEDR, LOW);
}
}
}

If you press BUTR the LEDR has to blink.
If you press BUTL the LEDL has to blink.
If you press BUTC the LEDR and the LEDL have to blink.
I don't use delay, but I think, that I have problems with asynchrony.

Answer 1

Thanks, Martin Taylor. I have warning, that millis() > 0 is always true. But I write millis() % 1000 == 0