Number of Shortest paths

AtCoder

IDabc211_d

Time2000ms

Memory256MB

Difficulty—

The Republic of AtCoder has $N$ cities numbered $1$ through $N$ and $M$ roads numbered $1$ through $M$. Using Road $i$, you can travel from City $A_i$ to $B_i$ or vice versa in one hour. How many paths are there in which you can get from City $1$ to City $N$ as early as possible? Since the count can be enormous, print it modulo $(10^9 + 7)$. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $0 \leq M \leq 2\times 10^5$ * $1 \leq A_i < B_i \leq N$ * The pairs $(A_i, B_i)$ are distinct. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

Output #1

2

The shortest time needed to get from City $1$ to City $4$ is $2$ hours, which is achieved by two paths: $1 \to 2 \to 4$ and $1 \to 3 \to 4$.

Input #2

Output #2

1

The shortest time needed to get from City $1$ to City $4$ is $3$ hours, which is achieved by one path: $1 \to 3 \to 2 \to 4$.

Input #3

2 0

Output #3

0

It is impossible to get from City $1$ to City $2$, in which case you should print $0$.

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Number of Shortest paths",
    "description": {
      "content": "The Republic of AtCoder has $N$ cities numbered $1$ through $N$ and $M$ roads numbered $1$ through $M$. Using Road $i$, you can travel from City $A_i$ to $B_i$ or vice versa in one hour. How many path",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc211_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The Republic of AtCoder has $N$ cities numbered $1$ through $N$ and $M$ roads numbered $1$ through $M$.\nUsing Road $i$, you can travel from City $A_i$ to $B_i$ or vice versa in one hour.\nHow many path...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments