D

#include <cstdio>
#include <algorithm>
#include <utility>
#include <cassert>
#include <vector>

using namespace std;

const int MOD = 1000000007, N = 1000005;

int n, m, k, ans, degs[N];

#define forn(i,n) for(int i = 0; i < (int) n; i++)

inline int add(int a, int b) { a += b; if (a >= MOD) a -= MOD; return a;}

int main(){
    degs[0] = 1;
    forn(i, N) {
        if (!i) continue;
        degs[i] = add(degs[i-1], degs[i-1]);
    }
    scanf("%d %d %d\n", &n, &m, &k);
    vector < pair<int,int> > edges;
    forn(i, m) {
        int a, b;
        scanf("%d %d", &a, &b);
        if (b - a != 1 && b - a != k + 1) {
            puts("0");
            return 0;
        }
        if (b - a == k + 1) edges.push_back(make_pair(a, b));
    }
    sort(edges.begin(), edges.end()); m = edges.size();
    if (k == 0 || k >= n - 1) {
        puts("1");
        return 0;
    }
    forn(i, m) {
        if (!(edges[i].first >= edges[0].first && edges[i].first < edges[0].second)) {
            puts("0");
            return 0;
        }
    }
        if (edges.size() == 0) ++ans;
    forn(i, n) {
        int f = i + 1, s = i + k + 2, cnt = m;
        if (s > n || (m > 0 && f > edges[0].first)) break;
        if (m > 0 && !(f <= edges[0].first && edges[m-1].first < s)) continue;
        if (m > 0 && f == edges[0].first) cnt--;
        s = min(s, n - k);
        ans = add(ans,degs[s - f - cnt - 1]);
    }
    printf("%d\n", ans);
}