#![allow(unused)]

use kyoproio::*;
use std::{
    collections::*,
    io::{self, prelude::*},
    iter,
    mem::{replace, swap},
};

fn main() -> io::Result<()> {
    std::thread::Builder::new()
        .stack_size(10 * 1024 * 1024)
        .spawn(solve)?
        .join()
        .unwrap();
    Ok(())
}

fn solve() {
    let stdin = io::stdin();
    let mut kin = KInput::new(stdin.lock());
    let stdout = io::stdout();
    let mut out = io::BufWriter::new(stdout.lock());
    macro_rules! output {($($args:expr),+) => { write!(&mut out, $($args),+) }; }
    macro_rules! outputln {
        ($($args:expr),+) => { output!($($args),+); outputln!(); };
        () => { output!("\n"); if cfg!(debug_assertions) { out.flush(); } }
    }

    let (n, m, x): (usize, usize, u64) = kin.input();
    let mut mat = vec![[0u64; W]; 30 + m];
    for i in 0..30 {
        mat[i][n / W] |= (x >> i & 1) << n % W;
    }
    for j in 0..n {
        let a: u64 = kin.input();
        for i in 0..30 {
            mat[i][j / W] |= (a >> i & 1) << j % W;
        }
    }
    for i in 0..m {
        let (t, l, r): (u64, usize, usize) = kin.input();
        let i = i + 30;
        mat[i][n / W] |= t << n % W;
        for j in l - 1..r {
            mat[i][j / W] |= 1 << j % W;
        }
    }
    let rank = elimination_f2(&mut mat);
    'outer: for r in &mut mat {
        if r[n / W] & 1 << n % W > 0 {
            r[n / W] ^= 1 << n % W;
            for j in 0..W {
                if r[j] != 0 {
                    continue 'outer;
                }
            }
            outputln!("0");
            return;
        }
    }
    outputln!("{}", mod_pow(2, (n - rank) as i64, 1e9 as i64 + 7));
}

const W: usize = 6;
fn elimination_f2(a: &mut [[u64; W]]) -> usize {
    let n = a.len();
    let mut k = 0;
    for i in 0..n {
        if let Some(j) = (k..n).find(|&j| a[j][i / W] >> i % W & 1 != 0) {
            a.swap(k, j);
            for l in (0..n).filter(|&l| l != k) {
                if a[l][i / W] >> i % W & 1 > 0 {
                    for b in 0..W {
                        a[l][b] ^= a[k][b];
                    }
                }
            }
            k += 1;
        }
    }
    k
}
pub fn mod_pow(mut a: i64, mut b: i64, m: i64) -> i64 {
    let mut y = 1;
    while b > 0 {
        if b & 1 == 1 {
            y = y * a % m;
        }
        a = a * a % m;
        b >>= 1;
    }
    y
}

// -----------------------------------------------------------------------------
pub mod kyoproio {
    #![warn(unused)]
    use std::io::prelude::*;
    pub trait Input {
        fn str(&mut self) -> &str;
        fn bytes(&mut self) -> &[u8] {
            self.str().as_ref()
        }
        fn input<T: InputParse>(&mut self) -> T {
            T::input(self)
        }
        fn iter<T: InputParse>(&mut self) -> Iter<T, Self> {
            Iter(self, std::marker::PhantomData)
        }
        fn seq<T: InputParse, B: std::iter::FromIterator<T>>(&mut self, n: usize) -> B {
            self.iter().take(n).collect()
        }
    }
    pub struct KInput<R> {
        src: R,
        buf: String,
        pos: usize,
    }
    impl<R: BufRead> KInput<R> {
        pub fn new(src: R) -> Self {
            Self {
                src,
                buf: String::with_capacity(1024),
                pos: 0,
            }
        }
    }
    impl<R: BufRead> Input for KInput<R> {
        fn str(&mut self) -> &str {
            loop {
                if self.pos >= self.buf.len() {
                    self.pos = 0;
                    self.buf.clear();
                    if self.src.read_line(&mut self.buf).expect("io error") == 0 {
                        return &self.buf;
                    }
                }
                let range = self.pos
                    ..self.buf[self.pos..]
                        .find(|c: char| c.is_ascii_whitespace())
                        .map(|i| i + self.pos)
                        .unwrap_or_else(|| self.buf.len());
                self.pos = range.end + 1;
                if range.end > range.start {
                    return &self.buf[range];
                }
            }
        }
    }
    pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>);
    impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> {
        type Item = T;
        fn next(&mut self) -> Option<Self::Item> {
            Some(self.0.input())
        }
    }
    pub trait InputParse: Sized {
        fn input<I: Input + ?Sized>(input: &mut I) -> Self;
    }
    macro_rules! from_str_impl {
        { $($T:ty)* } => {
            $(impl InputParse for $T {
                fn input<I: Input + ?Sized>(input: &mut I) -> Self {
                    input.str().parse::<$T>().expect("parse error")
                }
            })*
        };
    }
    from_str_impl! {
        String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128
    }
    macro_rules! tuple_impl {
        ($H:ident $($T:ident)*) => {
            impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) {
                fn input<I: Input + ?Sized>(input: &mut I) -> Self {
                    ($H::input(input), $($T::input(input)),*)
                }
            }
            tuple_impl!($($T)*);
        };
        () => {};
    }
    tuple_impl!(A B C D E F G);
}