矩阵运算模板

#include <bits/stdc++.h>
using namespace std;

#define FIN             freopen("input.txt","r",stdin)
#define FOUT            freopen("output.txt","w",stdout)
#define lson            l, mid, (rt << 1)
#define rson            mid + 1, r, (rt << 1 | 1)
#define __mid__         int mid = (l + r) >> 1

typedef __int64 LL;

const int MAXN = 100000 + 5;
const int MOD = 1e9 + 7;

int N, M, tp, L, R, X;

struct Mat {
    static const int MX = 2;
    int v[MX][MX];
    void O() {
        memset(v, 0, sizeof(v));
    }
    void E() {
        O();
        for(int i = 0; i < MX; i++) v[i][i] = 1;
    }
    Mat operator + (const Mat& e) const {
        Mat ret; ret.O();
        for(int i = 0; i < MX; i++) {
            for(int j = 0; j < MX; j++) {
                ret.v[i][j] = ((LL)v[i][j] + e.v[i][j]) % MOD;
            }
        }
        return ret;
    }
    Mat operator - (const Mat& e) const {
        Mat ret; ret.O();
        for(int i = 0; i < MX; i++) {
            for(int j = 0; j < MX; j++) {
                ret.v[i][j] = ((LL)v[i][j] - e.v[i][j] + MOD) % MOD;
            }
        }
        return ret;
    }
    Mat operator * (const Mat& e) const {
        Mat ret; ret.O();
        for(int k = 0; k < MX; k++) {
            for(int i = 0; i < MX; i++) {
                if(v[i][k] == 0) continue;
                for(int j = 0; j < MX; j++) {
                    ret.v[i][j] = (ret.v[i][j] + (LL) v[i][k] * e.v[k][j]) % MOD;
                }
            }
        }
        return ret;
    }
    Mat operator ^ (int b) const {
        Mat a, ret; ret.E();
        memcpy(a.v, v, sizeof(v));
        while(b > 0) {
            if(b & 1) ret = ret * a;
            a = a * a;
            b >>= 1;
        }
        return ret;
    }
} ini, tra, mat;

struct Seg {
    Mat sum, tag;
    bool col;
} seg[MAXN * 3];
inline void pushUp(int rt) {
    seg[rt].sum = seg[rt << 1].sum + seg[rt << 1 | 1].sum;
}
inline void down(int rt, int fa) {
    seg[rt].col = seg[fa].col;
    seg[rt].sum = seg[fa].tag * seg[rt].sum;
    seg[rt].tag = seg[fa].tag * seg[rt].tag;
}
inline void pushDown(int rt) {
    if(seg[rt].col) {
        down(rt << 1, rt);
        down(rt << 1 | 1, rt);
        seg[rt].tag.E();
        seg[rt].col = false;
    }
}
void build(int l, int r, int rt) {
    seg[rt].tag.E();
    seg[rt].col = false;
    if(l == r)  {
        scanf("%d", &X);
        mat = tra ^ (X - 1);
        seg[rt].sum = mat * ini;
        return;
    }
    __mid__;
    build(lson);
    build(rson);
    pushUp(rt);
}
void update(int l, int r, int rt) {
    if(L <= l && r <= R) {
        seg[rt].sum = mat * seg[rt].sum;
        seg[rt].tag = mat * seg[rt].tag;
        seg[rt].col = true;
        return;
    }
    __mid__;
    pushDown(rt);
    if(L <= mid) update(lson);
    if(R > mid) update(rson);
    pushUp(rt);
}
int query(int l, int r, int rt) {
    if(L <= l && r <= R) {
        return seg[rt].sum.v[0][0];
    }
    __mid__;
    pushDown(rt);
    int ret = 0;
    if(L <= mid) ret = query(lson);
    if(R > mid) ret += query(rson);
    return ret % MOD;
}

int main() {
#ifndef ONLINE_JUDGE
    FIN;
#endif // ONLINE_JUDGE
    ini.v[0][0] = 1, ini.v[0][1] = 0;
    ini.v[1][0] = 0, ini.v[1][1] = 0;
    tra.v[0][0] = 1, tra.v[0][1] = 1;
    tra.v[1][0] = 1, tra.v[1][1] = 0;
    scanf("%d %d", &N, &M);
    build(1, N, 1);
    while(M --) {
        scanf("%d %d %d", &tp, &L, &R);
        if(tp == 1) {
            scanf("%d", &X);
            mat = tra ^ X;  /// 因为把这个写在update里面，TLE了好几发...
            update(1, N, 1);
        } else {
            printf("%d\n", query(1, N, 1));
        }
    }
    return 0;
}