Money in Hand

AtCoder

IDabc286_d

Time3000ms

Memory256MB

Difficulty—

Takahashi has $N$ kinds of coins; specifically, for $1\leq i\leq N$, he has $B_i$ coins worth $A_i$ yen (the currency in Japan) each. Determine if Takahashi can pay exactly $X$ yen (without change) with the coins he currently has. ## Constraints * $1\leq N\leq 50$ * $1\leq X\leq 10^4$ * $1\leq A_i\leq 100$ * $1\leq B_i\leq 50$ * $A_i$ are pairwise distinct. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $X$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

2 19
2 3
5 6

Output #1

Yes

Takahashi has three $2$\-yen coins and six $5$\-yen coins. He can use two $2$\-yen coins and three $5$\-yen coins to pay exactly $2\times 2+5\times 3=19$ yen. Thus, `Yes` should be printed.

Input #2

2 18
2 3
5 6

Output #2

No

There is no combination of the coins that he can use to pay exactly $18$ yen. Thus, `No` should be printed.

Input #3

Output #3

Yes

He need not use all kinds of coins.

API Response (JSON)

{
  "problem": {
    "name": "Money in Hand",
    "description": {
      "content": "Takahashi has $N$ kinds of coins; specifically, for $1\\leq i\\leq N$, he has $B_i$ coins worth $A_i$ yen (the currency in Japan) each. Determine if Takahashi can pay exactly $X$ yen (without change) wi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc286_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $N$ kinds of coins; specifically, for $1\\leq i\\leq N$, he has $B_i$ coins worth $A_i$ yen (the currency in Japan) each.\nDetermine if Takahashi can pay exactly $X$ yen (without change) wi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments