#include <bits/stdc++.h>

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;
using u128 = unsigned __int128;

template<class Info, class Tag>
struct LazySegmentTree {
    int n;
    std::vector<Info> info;
    std::vector<Tag> tag;
    LazySegmentTree() : n(0) {}
    LazySegmentTree(int n_, Info v_ = Info()) {
        init(n_, v_);
    }
    template<class T>
    LazySegmentTree(std::vector<T> init_) {
        init(init_);
    }
    void init(int n_, Info v_ = Info()) {
        init(std::vector(n_, v_));
    }
    template<class T>
    void init(std::vector<T> init_) {
        n = init_.size();
        info.assign(4 << std::__lg(n), Info());
        tag.assign(4 << std::__lg(n), Tag());
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                info[p] = init_[l];
                return;
            }
            int m = (l + r) / 2;
            build(2 * p, l, m);
            build(2 * p + 1, m, r);
            pull(p);
        };
        build(1, 0, n);
    }
    void pull(int p) {
        info[p] = info[2 * p] + info[2 * p + 1];
    }
    void apply(int p, const Tag &v) {
        info[p].apply(v);
        tag[p].apply(v);
    }
    void push(int p) {
        apply(2 * p, tag[p]);
        apply(2 * p + 1, tag[p]);
        tag[p] = Tag();
    }
    void modify(int p, int l, int r, int x, const Info &v) {
        if (r - l == 1) {
            info[p] = v;
            return;
        }
        int m = (l + r) / 2;
        push(p);
        if (x < m) {
            modify(2 * p, l, m, x, v);
        } else {
            modify(2 * p + 1, m, r, x, v);
        }
        pull(p);
    }
    void modify(int p, const Info &v) {
        modify(1, 0, n, p, v);
    }
    Info rangeQuery(int p, int l, int r, int x, int y) {
        if (l >= y || r <= x) {
            return Info();
        }
        if (l >= x && r <= y) {
            return info[p];
        }
        int m = (l + r) / 2;
        push(p);
        return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
    }
    Info rangeQuery(int l, int r) {
        return rangeQuery(1, 0, n, l, r);
    }
    void rangeApply(int p, int l, int r, int x, int y, const Tag &v) {
        if (l >= y || r <= x) {
            return;
        }
        if (l >= x && r <= y) {
            apply(p, v);
            return;
        }
        int m = (l + r) / 2;
        push(p);
        rangeApply(2 * p, l, m, x, y, v);
        rangeApply(2 * p + 1, m, r, x, y, v);
        pull(p);
    }
    void rangeApply(int l, int r, const Tag &v) {
        return rangeApply(1, 0, n, l, r, v);
    }
    template<class F>
    int findFirst(int p, int l, int r, int x, int y, F &&pred) {
        if (l >= y || r <= x) {
            return -1;
        }
        if (l >= x && r <= y && !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        push(p);
        int res = findFirst(2 * p, l, m, x, y, pred);
        if (res == -1) {
            res = findFirst(2 * p + 1, m, r, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int l, int r, F &&pred) {
        return findFirst(1, 0, n, l, r, pred);
    }
    template<class F>
    int findLast(int p, int l, int r, int x, int y, F &&pred) {
        if (l >= y || r <= x) {
            return -1;
        }
        if (l >= x && r <= y && !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        push(p);
        int res = findLast(2 * p + 1, m, r, x, y, pred);
        if (res == -1) {
            res = findLast(2 * p, l, m, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int l, int r, F &&pred) {
        return findLast(1, 0, n, l, r, pred);
    }
};

constexpr i64 inf = 1E18;

struct Tag {
    i64 cm = 0LL;
    i64 add = 0LL;
    
    void apply(const Tag &t) & {
        cm = std::max(cm, t.cm - add);
        add += t.add;
    }
};

struct Info {
    i64 max = 0LL;
    
    void apply(const Tag &t) & {
        max = std::max(max, t.cm) + t.add;
    }
};

Info operator+(const Info &a, const Info &b) {
    return {std::max(a.max, b.max)};
}

i64 play_game(i64 N, int Q, i64 K, std::vector<i64> L, std::vector<i64> R) {
    std::vector<i64> val {0LL, K};
    std::vector<std::pair<i64, int>> e;
    for (int i = 0; i < Q; i++) {
        R[i]++;
        e.emplace_back(L[i], 1);
        e.emplace_back(R[i], -1);
        val.push_back(L[i] % K);
        val.push_back(R[i] % K);
    }
    std::sort(e.begin(), e.end());
    
    std::sort(val.begin(), val.end());
    val.erase(std::unique(val.begin(), val.end()), val.end());
    
    const int m = val.size() - 1;
    
    LazySegmentTree<Info, Tag> seg(m);
    auto work1 = [&](i64 l, i64 r, int a) {
        l = std::lower_bound(val.begin(), val.end(), l) - val.begin();
        r = std::lower_bound(val.begin(), val.end(), r) - val.begin();
        i64 v = seg.rangeQuery(0, m).max;
        seg.rangeApply(l, r, {v - a, a});
    };
    auto work = [&](i64 l, i64 r, int a) {
        if (l == r) {
            return;
        }
        if (l / K == (r - 1) / K) {
            work1(l % K, (r - 1) % K + 1, a);
        } else {
            work1(l % K, K, a);
            i64 t = (r - 1) / K - l / K - 1;
            if (t > 0) {
                i64 v = seg.rangeQuery(0, m).max;
                seg.rangeApply(0, m, {v - a, a * t});
            }
            work1(0, (r - 1) % K + 1, a);
        }
    };
    
    i64 lst = 0;
    int cur = 0;
    for (auto [x, t] : e) {
        work(lst, x, cur);
        cur += t;
        lst = x;
    }
    
    return seg.rangeQuery(0, m).max;
}