How do I alternate between using the rising and falling edge of a button interrupt in STM32F4?

Question

Button presses must alternate between two states:

1.) LED will turn ON in the rising edge of the button and keeps ON in the falling edge.

2.) LED will turn OFF in the falling edge of the next button press.

Button and LED Behavior

This is the main function of what I tried but the LED turns off only on button press:

volatile unsigned int pressed;
volatile unsigned int state;
int main(void){
    pressed = 0;
    state = 0;
    LD_Init();
    Interrupt_Init();
    /* Loop forever */
    while(1) {
        if (pressed) {
            if (state == 0) {
                EXTI->FTSR |= (1<<13); // Enable EXTI on Falling edge
                EXTI->RTSR &= ~(1<<13); // Disable EXTI on Rising edge
            }
            if  (state == 1){
                EXTI->FTSR &= ~(1<<13); // Disable EXTI on Falling edge
                EXTI->RTSR |= (1<<13); // Enable EXTI on Rising edge
            }
            GPIOA->ODR ^= (1<<5);
            pressed = 0;
            state = !state;
        }
    }
}
void EXTI15_10_IRQHandler(void){
    pressed = 1;
    EXTI->PR |= (1<<13); // Clear PR to re-enable EXTI interrupt
}