1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
| #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD = 1000000007;
const int MAXN = 200010;
ll powmod(ll a, ll b, ll mod) {
ll res = 1;
a %= mod;
for (; b; b >>= 1) {
if (b & 1) res = res * a % mod;
a = a * a % mod;
}
return res;
}
class Fenwick {
public:
vector<ll> tree;
int n;
Fenwick(int _n) : n(_n), tree(_n + 2, 0) {}
void update(int idx, ll val) {
idx++;
while (idx <= n + 1) {
tree[idx] = (tree[idx] + val) % MOD;
idx += idx & -idx;
}
}
ll query(int idx) {
idx++;
ll sum = 0;
while (idx > 0) {
sum = (sum + tree[idx]) % MOD;
idx -= idx & -idx;
}
return sum;
}
ll query(int l, int r) {
if (l > r) return 0;
return (query(r) - query(l - 1) + MOD) % MOD;
}
};
class SegMax {
public:
vector<int> tree;
int n;
SegMax(int _n) : n(_n), tree(4 * _n + 10, 0) {}
void build(int node, int start, int end, const vector<int>& a) {
if (start == end) {
tree[node] = a[start];
return;
}
int mid = (start + end) / 2;
build(2 * node, start, mid, a);
build(2 * node + 1, mid + 1, end, a);
tree[node] = max(tree[2 * node], tree[2 * node + 1]);
}
int query(int node, int start, int end, int l, int r) {
if (r < start || end < l) return -1;
if (l <= start && end <= r) return tree[node];
int mid = (start + end) / 2;
int p1 = query(2 * node, start, mid, l, r);
int p2 = query(2 * node + 1, mid + 1, end, l, r);
if (p1 == -1) return p2;
if (p2 == -1) return p1;
return max(p1, p2);
}
};
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int t;
cin >> t;
for (int cas = 0; cas < t; ++cas) {
int n, m;
cin >> n >> m;
vector<int> a(n + 1);
for (int i = 1; i <= n; ++i) cin >> a[i];
SegMax sm(n);
sm.build(1, 1, n, a);
vector<int> M(n + 1, -1);
int maxl = 0;
bool iszero = false;
for (int i = 0; i < m; ++i) {
int l, r;
cin >> l >> r;
M[r] = max(M[r], l);
maxl = max(maxl, l);
if (sm.query(1, 1, n, l, r) == 0) iszero = true;
}
if (iszero) {
cout << 0 << '\n';
continue;
}
vector<int> last_forced(n + 1, 0);
for (int i = 1; i <= n; ++i) {
if (a[i] == 10) last_forced[i] = i;
else last_forced[i] = last_forced[i - 1];
}
vector<ll> Q(n + 1, 1);
Q[0] = 1;
for (int i = 1; i <= n; ++i) {
if (a[i] == 10) Q[i] = 1;
else Q[i] = Q[i - 1] * (10LL - a[i]) % MOD;
}
vector<ll> DP(n + 1, 0);
DP[0] = 1;
Fenwick ft(n);
ll val = DP[0] * powmod(Q[0], MOD - 2, MOD) % MOD;
ft.update(0, val);
ll run = -1;
for (int i = 1; i <= n; ++i) {
run = max(run, (ll)M[i - 1]);
int mj_seg = max(0LL, run);
int mj = max(mj_seg, last_forced[i - 1]);
ll qsum = ft.query(mj, i - 1);
ll temp = qsum * Q[i - 1] % MOD;
DP[i] = (ll)a[i] * temp % MOD;
val = DP[i] * powmod(Q[i], MOD - 2, MOD) % MOD;
ft.update(i, val);
}
vector<ll> S(n + 2, 1);
for (int i = n; i >= 1; --i) {
S[i] = S[i + 1] * (10LL - a[i]) % MOD;
}
ll numer = 0;
for (int i = 0; i <= n; ++i) {
if (i >= maxl) {
numer = (numer + DP[i] * S[i + 1] % MOD) % MOD;
}
}
ll inv10 = powmod(10LL, MOD - 2, MOD);
ll inv10n = powmod(inv10, n, MOD);
ll ans = numer * inv10n % MOD;
cout << ans << '\n';
}
return 0;
}
|